Motion sensing by monitoring intensity of light redirected by an intensity pattern

ABSTRACT

Systems and techniques are described for measuring displacement of a moving mass by combining (i) information obtained from scanning, using a beam of light, an intensity pattern disposed on a surface of the mass, with (ii) information obtained when a coil interacts with a magnet attached to the moving mass.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of and claims priority toU.S. patent application Ser. No. 15/674,260, filed Aug. 10, 2017, whichclaims priority to U.S. Provisional Application Ser. No. 62/396,010,filed Sep. 16, 2016, and to U.S. Provisional Application Ser. No.62/396,030, filed Sep. 16, 2016, and to U.S. Provisional ApplicationSer. No. 62/396,022, filed Sep. 16, 2016. The disclosure of all relatedapplications is incorporated herein by reference in their entirety.

TECHNICAL FIELD

The present disclosure is generally related to motion sensing. Forexample, aspects of the present disclosure are related to measuringdisplacement of a mass by using an array of beams for scanning a binaryintensity pattern disposed on a surface of the mass. As another example,aspects of the present disclosure are related to measuring displacementof a moving mass by combining (i) information obtained from scanning,using a beam of light, an intensity pattern disposed on a surface of themass, with (ii) information obtained when a coil interacts with a magnetattached to the moving mass. As yet another example, aspects of thepresent disclosure are related to measuring displacement of a mass byilluminating an intensity pattern disposed on a surface of the mass withan array of beams and monitoring intensity of each of the beams that isredirected by the intensity pattern.

BACKGROUND

A haptic engine (also referred to as a vibration module) is a linearresonant actuator that determines one of acceleration, velocity anddisplacement of a moving mass. Either one of electrical sensing ormagnetic sensing can be conventionally used for measuring displacementsof the mass moving in the haptic engine. An example of electricalsensing, that is referred to as back electromotive force (bEMF) sensing,is based on sensing current-voltage of a coil that interacts with amagnet attached to the moving mass. For certain applications, accuracyof an absolute value of displacement measured by bEMF sensing may beinsufficient because the coil's resistance changes with temperature. Anexample of magnetic sensing, that is referred to as Hall sensing, isbased on sensing Hall voltages using Hall sensors that interact with amagnet attached to the moving mass. A displacement measuring systembased on conventional Hall sensing can be expensive to calibrate as theconventional Hall sensing uses a look-up-table calibration to linearizedisplacement sensitivity. Additionally, conventional Hall sensing canhave displacement sensitivity dead-zones when a Z-offset between theHall sensors and the magnet exceeds a small Z-offset threshold.Conventional Hall sensing is also susceptible to interference fromexternal magnetic fields.

Some of the above issues are remedied if measuring displacement of amass moving in a haptic engine is performed using optical sensing. Forinstance, a conventional optical system can be used in conjunction withconditioning electronics, for measuring displacements of a mass in avibration module. Such a conventional optical system includes a lightemitting diode (LED) module, a striped optical pattern attached to themoving mass, and a photodetector array module. In such a vibrationmodule, position of the striped optical pattern can be determinedrelative to a beam provided by an LED module. The photodetector arraymodule is used to image the striped optical pattern illuminated by thebeam. Each of (i) a bias used to power the LED module and (ii) an outputsignal of the photodetector array module is conditioned by a signalprocessing module that is configured based on a conventional transceiverarchitecture. As part of the conventional transceiver architecture, thesignal processing module operates essentially in class-A mode and,hence, it includes numerous analog circuits, e.g., op-amps, digitalPOTs, and trans-inductance amplifiers (TIAs). As such, the signalprocessing module, operated in such a conventional transceiverarchitecture, is power hungry, and hence it can be costly to operate.Further note that, because a photodetector array is used to image thestriped optical pattern illuminated by a single LED, the size of thevibration module in the Z-direction tends to grow unnecessarily in orderto facilitate optical focusing between the LED, the striped opticalpattern, and the photodetector array.

SUMMARY

In this disclosure, technologies are described for measuringdisplacement of a mass by using an array of beams for scanning a binaryintensity pattern disposed on a surface of the mass. The array of beamscan be provided by an array of vertical cavity surface emitting lasers(VCSELs), and the binary intensity pattern includes at least an edgeformed between two portions of the surface of the mass that havedifferent reflectivities. In this manner, a displacement of the mass canbe measured based on changes of reflected light intensity caused by arelative movement between the binary intensity pattern and the VCSELarray. Accuracy of the disclosed displacement measuring technique isdetermined by the geometry of the binary intensity pattern and thegeometry of the VCSEL array.

Further in this disclosure, technologies are described for measuringdisplacement of a moving mass by combining (i) information obtained fromscanning, using a beam of light, an intensity pattern disposed on asurface of the mass, with (ii) information obtained when a coilinteracts with a magnet attached to the moving mass. The beam of lightcan be provided by a VCSEL. The intensity pattern includes two or moretiles supported by the mass, the tiles being configured to spatiallymodulate intensity of light redirected to a photodetector, as individualones of the tiles are sequentially illuminated by the beam of light whenthe intensity pattern is displaced along with the mass relative to thebeam of light. An intensity signal issued by the photodetector relatesto the spatially modulated intensity of the redirected light.Additionally, a bEMF signal issued by the coil concurrently with theintensity signal relates to a spatially dependent bEMF induced in thecoil due to the motion relative to the coil of the magnet that isattached to the mass. Information from the intensity signal is combinedwith information from the bEMF signal to determine both absolute valueand direction of a displacement of the intensity pattern relative to thebeam of light. Note that the displacement determined in this manner canbe resolved at a scale smaller than what the size of the tiles of theintensity pattern would allow on its own.

Furthermore in this disclosure, technologies are described for measuringdisplacement of a mass by (i) illuminating an intensity pattern disposedon a surface of the mass with an array of beams, and (ii) monitoringintensity of each of the beams that is redirected by the intensitypattern. For instance, an array of VCSELs can be time multiplexed andused to scan an intensity pattern with respective beams emitted by theVCSELs of the array. In this manner, beams that have spatially modulatedintensity are redirected by the intensity pattern to a singlephoto-diode operated in charge integration mode. A photo-diode signalrelates to changes in intensity of each of the redirected beams and canbe used to decode a corresponding motion vector of the intensity patternthat is moving along with the mass.

A first aspect of the disclosure can be implemented as a displacementmeasuring system that includes a vertical cavity surface emitting laser(VCSEL) array including two or more vertical cavity surface emittinglasers (VCSELs) distributed along a first direction; and an opticalpattern supported by a mass, the optical pattern having two portionsthat form an edge oriented along a second direction that crosses thefirst direction, the two portions of the optical pattern havingdifferent reflectivities. Here, the VCSEL array is spaced apart from theoptical pattern and arranged such that, during operation of thedisplacement measuring system, the VCSEL array illuminates the opticalpattern, across the edge, with VCSEL light emitted by the VCSEL array.The displacement measuring system also includes a photodetector spacedapart from the optical pattern and arranged such that, during operationof the displacement measuring system, the photodetector integrates theVCSEL light that is redirected by the optical pattern to thephotodetector and issues a photodetector signal from the integratedVCSEL light; and processing electronics to receive the photodetectorsignal and determine a displacement of the mass along the firstdirection based on a change in the photodetector signal caused by motionof the mass along a direction of motion that crosses the edge.

Implementations can include one or more of the following features. Insome implementations, the two or more VCSELs of the VCSEL array can bearranged in a row parallel to the first direction and separated by apitch. In some implementations, the two or more VCSELs of the VCSELarray can be arranged in two rows parallel to the first direction, eachof the rows includes two or more VCSELs that are separated by a pitch,and the two rows are staggered relative to each other along the firstdirection by half the pitch and separated from each other by aseparation. In either of these implementations, the pitch can be about asize of a beam spot of the VCSEL light impinging on the optical pattern.In some cases, the separation can be about a size of a beam spot of theVCSEL light impinging on the optical pattern.

Further in some cases, the two portions of the optical pattern can forma second edge orthogonal to the first edge; the VCSEL array can befurther arranged such that, during operation of the displacementmeasuring system, the VCSEL array illuminates the optical pattern acrossthe second edge with the VCSEL light. In this manner, the processingelectronics can determine a second displacement of the mass along adirection orthogonal to the first direction based on a second change inthe photodetector signal caused by motion of the mass along a seconddirection of motion that crosses the second edge. For example, a firstof the two portions of the optical pattern can be shaped as a rectangleand is surrounded by the second portion, such that the first edge is afirst side of the rectangle, and the second edge is a second side of therectangle; additionally, a length of the second edge can be longer thana length of the VCSEL array, and a length of the first edge is longerthan the separation between the two rows of the VCSEL array.

In some implementations, the system can include a second VCSEL arrayincluding two or more VCSELs distributed along the first direction.Here, the two portions of the optical pattern form a second edgeparallel to the first edge; the second VCSEL array is spaced apart fromthe mass and arranged such that, during operation of the displacementmeasuring system, the second VCSEL array illuminates the opticalpattern, across the second edge but not across the first edge, withVCSEL light emitted by the second VCSEL array; the photodetector furtherissues, during operation of the displacement measuring system, a secondphotodetector signal based on the VCSEL light emitted by the secondVCSEL array that is redirected by the optical pattern to thephotodetector. In this manner, the processing electronics can receivethe second photodetector signal and determine the displacement of themass along the first direction further based on a change in the secondphotodetector signal caused by the motion of the mass along thedirection of motion.

In some cases, the processing electronics can determine a first ratiosignal as a division of the first photodetector signal to the secondphotodetector signal, and a second ratio signal as a division of thesecond photodetector signal to the first photodetector signal; anddetermine the displacement of the mass along the first direction basedon respective changes, caused by the motion of the mass along thedirection of motion, in the first ratio signal and the second ratiosignal. For example, the processing electronics can determine thedisplacement of the mass along the first direction based on the smallerof the first ratio signal and the second ratio signal.

In other cases, the first VCSEL array and the second VCSEL array can bespaced apart from the mass by the same separation. In this manner, theprocessing electronics can determine a change of the separation betweenthe VCSEL arrays and the mass, based on a change in a common value ofthe first photodetector signal and second photodetector signal.

In some other cases, the first VCSEL array and the second VCSEL arraycan illuminate the optical pattern, during operation of the displacementmeasuring system, in a multiplexed manner. Additionally, thephotodetector can issue the respective first photodetector signal andsecond photodetector signal in the same multiplexed manner. For example,the VCSELs of the first VCSEL array and the second VCSEL array can emitlight of the same wavelength; and the VCSELs of the first VCSEL arrayilluminate the optical pattern when the VCSELs of the second VCSEL arraydo not, and the VCSELs of the second VCSEL array illuminate the opticalpattern when the VCSELs of the first VCSEL array do not, in a timemultiplexed manner. As another example, the VCSELs of the first VCSELarray can emit light of a first wavelength and the VCSELs of the secondVCSEL array emit light of a second wavelength different from the firstwavelength; and the VCSELs of the first VCSEL array and the second VCSELarray illuminate the optical pattern concurrently, in a wavelengthmultiplexed manner. Here, the photodetector can include a first sensorto output a first sensor signal, and a second sensor to output a secondsensor signal. Additionally, the processing electronics can concurrentlyissue (i) the first photodetector signal based on a first combination ofthe first sensor signal and the second sensor signal, the firstcombination being selective of the first wavelength, and (ii) the secondphotodetector signal based on a second combination of the first sensorsignal and the second sensor signal, the second combination beingselective of the second wavelength.

In yet other cases, the first VCSEL array and the second VCSEL array canhave the same length; a first of the two portions of the optical patternis shaped as a strip bounded by the first edge and the second edgeinside a second of the two portions; and a width of the strip is widerthan the common length of the VCSEL arrays.

In some implementations, one of the two portions of the optical patterncan be reflective and the other one of the two portions of the opticalpattern is absorptive. In some implementations, at least one of the twoportions of the optical pattern can be printed using ink that absorbs IRlight. In some implementations, one of the two portions of the opticalpattern can be coated with a multilayer reflection coating, and theother one of the two portions of the optical pattern is coated with amultilayer anti-reflection coating. In some implementations, one of thetwo portions of the optical pattern can have a reflectivity that is atleast twice as large as a reflectivity of the other one of the twoportions of the optical pattern. In some implementations, the VCSELlight emitted by the VCSELs can have wavelengths in a range from 700 nmto 1100 nm. In some implementations, the second direction can beorthogonal to the first direction. In some implementations, thedirection of motion can be parallel to the first direction.

Another aspect of the disclosure can be implemented as a 2D-displacementmeasuring system that includes two pairs of light-emitting element (LEE)arrays, each LEE array having two rows of light-emitting elements(LEEs), the rows of LEEs being parallel to a first direction, and eachLEE being configured to output collimated light; an optical patternsupported by a mass, the optical pattern having two portions that form arectangular edge, the rectangular edge having two sides parallel to thefirst direction, the two portions of the optical pattern havingdifferent reflectivities, where each LEE array illuminates the opticalpattern, across a corresponding corner of the rectangular edge, with thecollimated light output by the LEE array; a photodetector to separatelyintegrate the collimated light output by the respective LEE arraysredirected by the optical pattern to the photodetector, and issue twopairs of photodetector signals from the separately integrated lightoutput by the respective LEE arrays; and processing electronics toreceive the photodetector signals and determine displacements of themass along, and orthogonal to, the first direction based on changes inthe corresponding photodetector signals caused by motion of the mass.

Another aspect of the disclosure can be implemented as an angulardisplacement measuring system that includes three pairs oflight-emitting element (LEE) arrays, each LEE array having two rows oflight-emitting elements (LEEs), the rows of LEEs within each pair of LEEarrays being parallel to each other, and the rows of LEEs from differentpairs of LEE arrays forming an angle of 120° with each other; an opticalpattern supported around the perimeter of a wheel, the optical patternhaving two portions that form three rectangular edges, each rectangularedge having two sides parallel to the rows of LEEs when the rectangularedge is proximate to a pair of LEE arrays, the two portions of theoptical pattern having different reflectivities, where each LEE array ofthe proximate pair illuminates the optical pattern, across acorresponding corner of the rectangular edge, with collimated lightoutput by the LEE array; a photodetector to issue three pairs ofphotodetector signals based on the collimated light output by therespective pair of LEE arrays and redirected by the optical pattern tothe photodetector, each pair of photodetector signals including aperiodic photodetector signal; and processing electronics to receive thephotodetector signals and determine (i) an angular displacement of thewheel based on changes in the periodic photodetector signals caused byrotation of the wheel about a rotation axis of the wheel, and (ii) alateral displacement of the wheel based on changes in one or more of theremaining photodetector signals caused by translation of the wheel alongthe rotation axis.

Implementations of each of the 2D-displacement measuring system and theangular displacement measuring system can include one or more of thefollowing features. In some implementations, each LEE can include aVCSEL. In some implementations, each LEE can include a light sourceconfigured to emit un-collimated light; and collimating optics opticallycoupled with the light source to collimate the emitted light. In someimplementations, the photodetector can include a CMOS sensor array or aCCD sensor array.

Another aspect of the disclosure can be implemented as a haptic enginethat includes the mass and any of the foregoing displacement measuringsystems. In some implementations, a computing device can include thehaptic engine.

A second aspect of the disclosure can be implemented as a displacementmeasuring system that includes (i) a back electromotive force (bEMF)sensing system to acquire a first displacement signal that relates to atime dependence of a displacement of a mass, where the displacement isrelative to a datum of the displacement measuring system; (ii) anoptical sensing system including an intensity pattern that is coupledwith the mass and comprises two or more tiles separated from each otherby corresponding one or more tile borders, where the tile borders are atknown locations relative to each other; a light source that is at restrelative to the datum to illuminate the intensity pattern with a lightbeam, where multiple tile border crossings occur while the firstdisplacement signal is being acquired, and where a tile border crossingis said to occur when a tile border of the intensity pattern crossesthrough the light beam; and a photodetector that is at rest relative tothe datum to acquire an intensity signal corresponding to intensity ofthe light beam redirected to the photodetector from the intensitypattern, where the intensity signal is indicative of the tile bordercrossings; and (iii) a processor to spatially resolve the tile bordercrossings indicated by the intensity signal, at least in part, based onwhether the first displacement signal increases or decreases at a timewhen a tile border crossing has occurred; and determine the displacementof the mass based on the spatially resolved tile border crossings.

Implementations can include one or more of the following features. Insome implementations, the processor can determine a second displacementsignal using the spatially resolved tile border crossings; and determinethe displacement of the mass by combining the first displacement signaland the second displacement signal. In some cases, the processor candetermine a scale factor equal to a ratio of a change in the seconddisplacement signal over a predetermined time interval and a change inthe first displacement signal over the predetermined time interval;differentiate the first displacement signal; and scale thedifferentiated first displacement signal based on the scale factor priorto the combining of the first displacement signal and the seconddisplacement signal. Additionally, the processor can update the scalefactor when the first displacement signal over the predetermined timeinterval exceeds a threshold change. In some cases, the bEMF sensingsystem can sample the first displacement signal using a first samplingfrequency; and the optical sensing system can sample the intensitysignal using a second sampling frequency smaller than the first samplingfrequency, thereby samples of the second displacement signal have thesecond sampling frequency. In the latter cases, to perform the combiningof the first displacement signal and the second displacement signal, theprocessor can insert corresponding samples of the scaled differentiatedfirst displacement signal between samples of the second displacementsignal.

In some implementations, each tile can have a size larger than a beamspot formed by the light beam that illuminates the intensity pattern,and each tile is configured to redirect to the photodetector lighthaving an intensity different from an intensity of light redirected tothe photodetector by any of its adjacent tiles. In some cases, theintensity pattern can be a binary intensity pattern in which each tilehas only two adjacent tiles configured to redirect to the photodetectorlight having the same intensity. In other cases, each tile can be ahexagonal tile configured to redirect to the photodetector light havingan intensity level that is one of (i) a minimum intensity level, (ii) amaximum intensity level, (iii) a first intermediate intensity levelbetween the minimum intensity level and the maximum intensity level, and(iv) a second intermediate intensity level between the firstintermediate intensity level and the maximum intensity level.

In the latter cases, the first displacement signal acquired by the bEMFsensing system represents the time dependence of a component of thedisplacement of the mass along a first direction. As such, the processorcan (i) spatially resolve first tile border crossings indicated by theintensity signal based on whether the first displacement signalincreases or decreases at a time when a first tile border crossing hasoccurred along the first direction, and (ii) determine the component ofthe displacement of the mass along the first direction based on thespatially resolved first tile border crossings. Further, the processorcan (iii) spatially resolve second tile border crossings indicated bythe intensity signal based on changes between a pair of the minimumintensity level, the maximum intensity level, the first intermediateintensity level, and the second intermediate intensity level ofredirected light that is captured by the photodetector when a secondtile border crossing has occurred along a second direction orthogonal tothe first direction, and (iv) determine a component of the displacementof the mass along the second direction based on the spatially resolvedsecond tile border crossings. Also in the latter cases, the light sourcecan concurrently illuminate three tiles of the intensity pattern thatare adjacent to each other, one of the three adjacent tiles illuminatedwith the probe beam, and the other two of the three adjacent tilesrespectively illuminated with two reference light beams, the tworeference light beams spaced apart from the probe beam by a separationabout equal to a separation between adjacent tiles; and the probe beamand the reference light beams can illuminate the three adjacent tileswith substantially equal intensities. Here, the light source canconcurrently illuminate the three adjacent tiles in a time multiplexedmanner. Further here, the photodetector can acquire reference signalscorresponding to intensities of respective reference light beamsredirected to the photodetector from the intensity pattern, and theoptical sensing system can sample the reference signals using a thirdsampling frequency smaller than the second sampling frequency. Alsohere, the processor can compare measured values and expected values ofdifferences between intensity of the probe light beam redirected to thephotodetector from one of the three adjacent tiles and respective onesof the other two of the three adjacent tiles respectively illuminatedwith two reference light beams, and the light source can adjust theintensity of the probe light beam based on the compared differences.

In some implementations, the photodetector can include a thresholdmodule to apply one or more threshold values to each intensity value ofthe light beam redirected to, and measured by, the photodetector toissue a corresponding expected value of the intensity value. In somecases, the photodetector can include a filter to adaptively determinethe one or more threshold values. In other cases, the one or morethreshold values can be predetermined.

In some implementations, the photodetector can include a photodiode. Insome implementations, the light source can include a vertical cavitysurface emitting laser (VCSEL) to emit the probe beam. In someimplementations, the light source can include a light emitting diode(LED) to emit probe light; and beam-shaping optics to form the probebeam. In some implementations, the intensity pattern can be reflectiveto the probe light beam, and disposed on a surface of the mass.

In some implementations, the intensity pattern can be transparent to theprobe light beam, and the optical sensing system includes an opticalstructure having a first surface and a second, opposing surface, theintensity pattern is disposed on the first surface of the opticalstructure, and the optical structure is attached to a surface of themass adjacent the second surface of the optical structure. In somecases, the optical structure can include an array of micro-mirrorsdisposed between the first and second surfaces of the optical structure,and the micro-mirrors of the array are oriented to redirect to thephotodetector the light beam that impinges on the array of micro-mirrorsafter transmission through the intensity pattern. In some cases, theoptical structure can include solid material that is transparent to theprobe light beam. In the latter cases, the optical sensing system caninclude a diffusive film sandwiched between the second surface of theoptical structure and the surface of the mass, and the diffusive film isconfigured to redirect to the photodetector the light beam that impingeson the diffusive film after transmission through the intensity pattern.Also in the latter cases, the second surface of the optical structure isspaced apart from the surface of the mass by an air gap, and the secondsurface of the optical structure can include facets arranged to reflect,via total internal reflection (TIR), to the photodetector, the lightbeam that impinges on the facets after transmission through theintensity pattern. Also in the latter cases, the optical sensing systemcan include a diffusive material sandwiched between the second surfaceof the optical structure and the surface of the mass, and the secondsurface of the optical structure can include facets arranged todiffusely reflect, to the photodetector, the light beam that impinges onthe facets after transmission through the intensity pattern.

Another aspect of the disclosure can be implemented as a haptic enginethat includes the mass and a displacement measuring system summarizedabove. In some implementations, a computing device can include thehaptic engine.

A third aspect of the disclosure can be implemented as a method thatincludes a displacement measuring system that includes a vertical cavitysurface emitting laser (VCSEL) array including two or more (N_(TOT))vertical cavity surface emitting lasers (VCSELs) distributed along afirst direction; an intensity pattern that is coupled with a mass andincludes two or more tiles separated from each other by correspondingone or more tile borders, where the tile borders are at known locationsrelative to each other along the first direction, and where the VCSELarray is spaced apart from the intensity pattern and arranged such that,during operation of the displacement measuring system, the (N_(TOT))VCSELs of the array illuminate respective locations of the intensitypattern across at least one of the tile borders; a photodetector spacedapart from the intensity pattern and arranged such that, duringoperation of the displacement measuring system, the photodetector to (i)capture beams redirected to the photodetector from the (N_(TOT))illuminated locations of the intensity pattern, where each tile of theintensity pattern is configured to redirect to the photodetector lighthaving an intensity different from an intensity of light redirected tothe photodetector by its adjacent tiles, and (ii) issue a set of(N_(TOT)) intensity values corresponding to the respective capturedbeams; and a processor to determine (i) positions of the illuminatedlocations of the intensity pattern based on relative differences betweenthe intensity values of the issued set, and (ii) a displacement of themass along the first direction based on one or more changes of theintensity values of the set caused by motion of the mass along adirection of motion across the at least one of the tile borders.

Implementations can include one or more of the following features. Insome implementations, the photodetector is a single photodiode, and theVCSELs of the VCSEL array are configured to illuminate the intensitypattern in a time multiplexed manner. In some implementations, thephotodetector issues instances of the set of intensity values with asampling frequency (f_(S)), and the processor can obtain an intensitysignal as a sequence of the instances of the set of intensity values,the sequence having a frequency equal to the sampling frequency (f_(S)),and use the obtained intensity signal to determine the displacement ofthe mass along the first direction.

In some implementations, the VCSELs of the VCSEL array can be arrangedin a row parallel to the first direction and separated by a pitch (δ)configured such that at least two of the beams emitted by the VCSELarray can concurrently illuminate, along the first direction, a singletile of the intensity pattern. In some cases, the intensity pattern canhave a pattern period (P) along the first direction that is formed from(M≥2) different tiles, each tile of the pattern period being configuredto redirect to the photodetector light having an associated intensitylevel from among (M) corresponding different intensity levels, thepattern period satisfying the condition P>(N_(TOT)−1)δ, and for a motionof the mass that causes a maximum velocity (v_(MAX)) of the intensitypattern, a sampling frequency (f_(S)) satisfies the conditionf_(S)>2v_(MAX)/[(N_(TOT)−1)δ]. In some cases, the intensity pattern canhave a pattern period (P) along the first direction that is formed from(M≥2) different tiles, each tile of the pattern period being configuredto redirect to the photodetector light having an associated intensitylevel from among the (M) different intensity levels, the pattern periodsatisfying the condition P≤(N_(TOT)−1)δ, and, for a motion of the massthat causes a maximum velocity (v_(MAX)) of the intensity pattern, asampling frequency (f_(S)) satisfies the condition f_(S)>2v_(MAX)/P.

In some implementations, the VCSEL array can include two or more VCSELsdistributed along a second direction that crosses the first direction;the intensity pattern can include at least two or more tiles that formone or more tile borders across the first direction, and at least two ormore tiles that form one or more tile borders across the seconddirection, the tile borders being at known locations relative to eachother along the first and second directions, such that, during operationof the displacement measuring system, the VCSELs of the array illuminaterespective locations of the intensity pattern, across at least one ofthe tile borders along the first direction and across at least anotherone of the tile borders along the second direction; and the processorcan determine the displacement of the mass along the first directionbased on one or more changes of the intensity values of the set causedby motion of the mass along a direction of motion across the at leastone of the tile borders along the first direction and across the atleast another one of the tile borders along the second direction. Here,the VCSELs of the VCSEL array can be arranged in a first row parallel tothe first direction, the first row including (N_(X)) VCSELs separated bya first pitch (δ_(X)) configured such that at least two of the beamsemitted by the VCSEL array can concurrently illuminate, along the firstdirection, a single tile of the intensity pattern, and a second rowparallel to the second direction, the second row including (N_(Y))VCSELs separated by a second pitch (δ_(Y)) configured such that at leasttwo of the beams emitted by the VCSEL array can concurrently illuminate,along the second direction, a single tile of the intensity pattern.

In some cases of these implementations, the intensity pattern can have afirst pattern period (P_(X)) along the first direction that is formedfrom (M_(X)≥2) different tiles, each tile of the first pattern periodbeing configured to redirect to the photodetector light having anassociated intensity level from among (M_(X)) corresponding differentintensity levels, the first pattern period satisfying the conditionP_(X)>(N_(X)−1)δ_(X), and the intensity pattern can have a secondpattern period (P_(Y)) along the second direction that is formed from(M_(Y)≥2) different tiles, each tile of the second pattern period beingconfigured to redirect to the photodetector light having an associatedintensity level from among (M_(Y)) corresponding different intensitylevels, the second pattern period satisfying the conditionP_(Y)>(N_(Y)−1)δ_(Y). As such, for a motion of the mass that causes amaximum velocity (v_(MAX)) of the intensity pattern, a samplingfrequency (f_(S)) satisfies the conditionf_(S)>MAX{2v_(MAX,X)/[(N_(X)−1)δ_(X)], 2v_(MAX,Y)/[(N_(Y)−1)δ_(Y)]}.

In some cases of these implementations, the intensity pattern can have afirst pattern period (P_(X)) along the first direction that is formedfrom (M_(X)≥2) different tiles, each tile of the first pattern periodbeing configured to redirect to the photodetector light having anassociated intensity level from among (M_(X)) corresponding differentintensity levels, the first pattern period satisfying the conditionP_(X)≤(N_(X)−1)δ_(X), and the intensity pattern can have a secondpattern period (P_(Y)) along the second direction that is formed from(M_(Y)≥2) different tiles, each tile of the second pattern period beingconfigured to redirect to the photodetector light having an associatedintensity level from among (M_(Y)) corresponding different intensitylevels, the second pattern period satisfying the conditionP_(Y)≤(N_(Y)−1)δ_(Y). As such, for a motion of the mass that causes amaximum velocity (v_(MAX)) of the intensity pattern, a samplingfrequency (f_(S)) satisfies the condition f_(S)>MAX{2v_(MAX,X)/P_(X),2v_(MAX,Y)/P_(Y)}.

In some cases of these implementations, the intensity pattern can have afirst pattern period (P_(X)) along the first direction that is formedfrom (M_(X)≥2) different tiles, each tile of the first pattern periodbeing configured to redirect to the photodetector light having anassociated intensity level from among (M_(X)) corresponding differentintensity levels, the first pattern period satisfying the conditionP_(X)>(N_(X)−1)δ_(X), and the intensity pattern can have a secondpattern period (P_(Y)) along the second direction that is formed from(M_(Y)≥2) different tiles, each tile of the second pattern period beingconfigured to redirect to the photodetector light having an associatedintensity level from among (M_(Y)) corresponding different intensitylevels, the second pattern period satisfying the conditionP_(Y)≤(N_(Y)−1)δ_(Y). As such, for a motion of the mass that causes amaximum velocity (v_(MAX)) of the intensity pattern, a samplingfrequency (f_(S)) satisfies the conditionf_(S)>MAX{2v_(MAX,X)/[(N_(X)−1)δ_(X)], 2v_(MAX,Y)/P_(Y)}.

In some cases of these implementations, the intensity pattern can have afirst pattern period (P_(X)) along the first direction that is formedfrom (M_(X)≥2) different tiles, each tile of the first pattern periodbeing configured to redirect to the photodetector light having anassociated intensity level from among (M_(X)) corresponding differentintensity levels, the first pattern period satisfying the conditionP_(X)≤(N_(X)−1)δ_(X), and the intensity pattern can have a secondpattern period (P_(Y)) along the second direction that is formed from(M_(Y)≥2) different tiles, each tile of the second pattern period beingconfigured to redirect to the photodetector light having an associatedintensity level from among (M_(Y)) corresponding different intensitylevels, the second pattern period satisfying the conditionP_(Y)>(N_(Y)−1)δ_(Y). As such, for a motion of the mass that causes amaximum velocity (v_(MAX)) of the intensity pattern, a samplingfrequency (f_(S)) satisfies the condition f_(S)>MAX{2v_(MAX,X)/P_(X),2v_(MAX,Y)/[(N_(Y)−1)δ_(Y)]}.

Moreover, in these implementations, the processor can determine a totaldisplacement of the mass along the second direction that corresponds toa maximum displacement of the mass along the first direction; determinean angular misalignment of the intensity pattern based on the totaldisplacement of the mass along the second direction; and determine ascaling factor to scale the determined displacement of the mass alongthe first direction and the determined displacement of the mass alongthe second direction.

In some implementations, the intensity pattern can include a surfacethat is reflective to the beams emitted by the VCSEL array. In someimplementations, the intensity pattern can include a surface that istransparent to the beams emitted by the VCSEL array and is spatiallymodulated by the tiles; and an array of redirecting micro-structuresdisposed between the first surface and the mass, the redirectingmicro-structures of the array being oriented to redirect, by a foldingangle, to the photodetector, the beams emitted by the VCSEL array thatimpinge on the array of redirecting micro-structures after at least onetransmission through the first surface. In some cases, the system caninclude a mount including a surface onto which the VCSEL array and thephotodetector are disposed side-by-side to each other, where the foldingangle is an acute angle. In some cases, the system can include a mountincluding a first surface onto which the VCSEL array is disposed, and asecond surface angled to the first surface, the photodetector beingdisposed on the second surface, where the folding angle is substantiallya right angle.

In some implementations, to determine the positions of the illuminatedlocations of the intensity pattern, the processor can use the issued setof intensity values against a mapping of (A) sets of expected intensityvalues to (B) positions of illuminated locations of the intensitypattern.

Another aspect of the disclosure can be implemented as a displacementmeasuring system that includes a single light-emitting element (LEE); anintensity pattern that is coupled with a mass and includes three or moretiles separated from each other by corresponding one or more tileborders, where the tile borders are at known locations relative to eachother along a first direction, and where the LEE is spaced apart fromthe intensity pattern and arranged such that, during operation of thedisplacement measuring system, the LEE illuminates a location of theintensity pattern; a single photodiode spaced apart from the intensitypattern and arranged such that, during operation of the displacementmeasuring system, the photodiode to (i) capture a beam redirected to thephotodiode from the illuminated location of the intensity pattern, whereeach tile of the intensity pattern is configured to redirect to thephotodiode light having an intensity different by (A) a first amountfrom an intensity of light redirected to the photodiode by one of itsadjacent tiles, and (B) a second amount from another intensity of lightredirected to the photodiode by another one of its adjacent tiles, and(ii) issue a single intensity value corresponding to the captured beam;and a processor to determine (i) a position of the illuminated locationof the intensity pattern based on the issued intensity value, and (ii) adisplacement of the mass along the first direction based on changes ofthe intensity value caused by motion of the mass along a direction ofmotion across at least one of the tile borders.

Implementations of the above-summarized measuring system can include oneor more of the following features. In some implementations, theintensity pattern can have a pattern period (P) along the firstdirection that is formed from (M≥3) different tiles, each tile of thepattern period being configured to redirect to the photodiode lighthaving an associated intensity level from among (M) correspondingdifferent intensity levels. As such, for a motion of the mass thatcauses a maximum velocity (v_(MAX)) of the intensity pattern, thesampling frequency (f_(S)) satisfies the condition f_(S)>2v_(MAX)/P, andthe processor can obtain an intensity signal as a sequence of theintensity values, the sequence having a frequency equal to the samplingfrequency (f_(S)). In some implementations, to determine the positionsof the illuminated locations of the intensity pattern, the processor canuse the issued intensity value against a mapping of (A) expectedintensity values to (B) positions of illuminated locations of theintensity pattern.

Another aspect of the disclosure can be implemented as a haptic enginethat includes the mass and one of the displacement measuring systemssummarized above.

Another aspect of the disclosure can be implemented as an angulardisplacement measuring system that includes a light-emitting element(LEE) array including two or more (N_(TOT)) light-emitting elements(LEEs), each LEE being configured to output collimated light in the formof a beam; an intensity pattern that is disposed on a side wall surfaceof a wheel, the intensity pattern including tiles shaped as annulussectors, the tiles separated from each other by corresponding one ormore tile borders, where the tile borders are radially oriented at knownangular locations relative to each other, and where the LEE array isspaced apart from the intensity pattern and arranged such that, duringoperation of the angular displacement measuring system, the (N_(TOT))LEEs of the array output beams along a direction orthogonal to the sidewall surface and illuminate respective locations of the intensitypattern across at least one of the tile borders; a photodetector spacedapart from the intensity pattern and arranged such that, duringoperation of the angular displacement measuring system, thephotodetector (i) captures beams redirected along a radial directionthrough the rim surface of the wheel to the photodetector from the(N_(TOT)) illuminated locations of the intensity pattern, where eachtile of the intensity pattern is configured to redirect to thephotodetector light having an intensity different from an intensity oflight redirected to the photodetector by its adjacent tiles, and (ii)issues a set of (N_(TOT)) intensity values corresponding to therespective captured beams; and a processor to determine (i) positions ofthe illuminated locations of the intensity pattern based on relativedifferences between the intensity values of the issued set, and (ii) anangular displacement of the wheel based on one or more changes of theintensity values of the set caused by rotation of the wheel across theat least one of the tile borders.

Another aspect of the disclosure can be implemented as an angulardisplacement measuring system that includes a light-emitting element(LEE) array including two or more (N_(TOT)) light-emitting elements(LEEs), each LEE being configured to output collimated light in the formof a beam; an intensity pattern that is disposed on the rim surface of awheel, the intensity pattern includes tiles separated from each other bycorresponding one or more tile borders, where the tile borders areoriented either along the length, or the width, of the rim at knownlocations relative to each other, and where the LEE array is spacedapart from the intensity pattern and arranged such that, duringoperation of the angular displacement measuring system, the (N_(TOT))LEEs of the array output beams along a radial direction through the rimsurface of the wheel and illuminate respective locations of theintensity pattern across at least one of the tile borders; aphotodetector spaced apart from the intensity pattern and arranged suchthat, during operation of the angular displacement measuring system, thephotodetector (i) captures beams redirected to the photodetector fromthe (N_(TOT)) illuminated locations of the intensity pattern, where eachtile of the intensity pattern is configured to redirect to thephotodetector light having an intensity different from an intensity oflight redirected to the photodetector by its adjacent tiles, and (ii)issues a set of (N_(TOT)) intensity values corresponding to therespective captured beams; and a processor to determine (i) positions ofthe illuminated locations of the intensity pattern based on relativedifferences between the intensity values of the issued set, and (ii) anangular displacement, and a lateral displacement, of the wheel based onone or more changes of the intensity values of the set caused byrotation, and lateral translation, of the wheel across the at least oneof the tile borders.

Implementations of the above-summarized angular displacement measuringsystems can include one or more of the following features. In someimplementations, the beams redirected from the (N_(TOT)) illuminatedlocations of the intensity pattern to the photodetector can be tilted byan acute angle relative the radial direction along which the LEEs of thearray output the beams. In some implementations, the beams redirectedfrom the (N_(TOT)) illuminated locations of the intensity patternthrough a side wall surface of the wheel to the photodetector can betilted by a substantially right angle relative the radial directionalong which the LEEs of the array output the beams.

Another aspect of the disclosure can be implemented as a displacementmeasuring system that includes a light-emitting element (LEE) arrayincluding two or more (N_(TOT)) light-emitting elements (LEEs), each LEEbeing configured to output collimated light in the form of a beam; anintensity pattern that is disposed on a surface of an axle of a wheel,the intensity pattern includes tiles separated from each other bycorresponding one or more tile borders, where the tile borders areoriented either around, or along, the axle at known locations relativeto each other, and where the LEE array is spaced apart from theintensity pattern and arranged such that, during operation of theangular displacement measuring system, the (N_(TOT)) LEEs of the arrayoutput beams along a radial direction through the axle surface of theaxle and illuminate respective locations of the intensity pattern acrossat least one of the tile borders; a photodetector spaced apart from theintensity pattern and arranged such that, during operation of theangular displacement measuring system, the photodetector (i) capturesbeams redirected from the (N_(TOT)) illuminated locations of theintensity pattern to the photodetector, where each tile of the intensitypattern is configured to redirect to the photodetector light having anintensity different from an intensity of light redirected to thephotodetector by its adjacent tiles, where the beams redirected from the(N_(TOT)) illuminated locations of the intensity pattern to thephotodetector are tilted by an acute angle relative the radial directionalong which the LEEs of the array output the beams, and (ii) issues aset of (N_(TOT)) intensity values corresponding to the respectivecaptured beams; and a processor to determine (i) positions of theilluminated locations of the intensity pattern based on relativedifferences between the intensity values of the issued set, and (ii) anangular displacement, and a lateral displacement, of the wheel based onone or more changes of the intensity values of the set caused byrotation, and lateral translation, of the wheel across the at least oneof the tile borders.

Implementations of the above-summarized measuring systems can includeone or more of the following features. In some implementations, each LEEcan include a VCSEL. In some implementations, each LEE can include alight source configured to emit un-collimated light; and collimatingoptics optically coupled with the light source to collimate the emittedlight. In some implementations, the photodetector is a singlephotodiode; and the LEEs of the LEE array are configured to illuminatethe intensity pattern in a time multiplexed manner.

Another aspect of the disclosure can be implemented as a watch thatincludes one of the above-summarized angular displacement measuringsystems or displacement measuring systems.

Another aspect of the disclosure can be implemented as a computingdevice that includes one or more of the above summarized haptic engine,angular displacement measuring systems, or displacement measuringsystem.

The above-disclosed technologies can result in one or more of thefollowing potential advantages. For example, absolute positions of amoving mass, disposed in vibration modules, that are measured by thedisclosed displacement measuring systems can be used to effectivelycontrol saliency and prevent noise and damage. As such, accuratelymeasured displacement of the moving mass allows closed-loop control. Theclosed-loop control enables richer saliency vocabularies, compensationagainst aging degradation, and crash of, or damage to, the vibrationmodules. As another example, implementations of the discloseddisplacement measuring systems used for 1D motion sensing can beextended to 2D motion sensing, where displacements ΔX and ΔY of themoving mass can be concurrently measured.

As yet another example, thickness along the Z-axis of a vibration modulethat uses the disclosed displacement measuring systems can besignificantly reduced relative to a conventional vibration module,because the disclosed displacement measuring systems' VCSEL-basedoptical source does not need focusing, so it can be placed at anyarbitrary distance to the intensity pattern. As yet another example, avibration module that uses the disclosed displacement measuring systemscan be self-calibrated with the intensity pattern acting as displacementreference, so they do not need to be placed in a calibration tester likeconventional displacement measuring systems.

As yet another example, the disclosed displacement measuring systems canbe insensitive to Z-offset given by relative alignment/misalignmentbetween the moving mass and the VCSEL array. As yet another example, thedisclosed displacement measuring system can be insensitive totemperature change as it uses a ratiometric measurement technique.

As yet another example, the transceiver architecture of the discloseddisplacement measuring systems is configured to operate in pulse widthmodulation (PWM) mode which uses a reduced number of analog componentscompared to the class-A mode in which the transceiver architecture usedin a conventional vibration module is configured to operate.

Details of one or more implementations of the disclosed technologies areset forth in the accompanying drawings and the description below. Otherfeatures, aspects, descriptions and potential advantages will becomeapparent from the description, the drawings and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1C show aspects of a displacement measuring system.

FIG. 1D is an example of a timing diagram used by the displacementmeasuring system of FIGS. 1A-1C.

FIGS. 1E-1F shows aspects of a haptic system that uses the displacementmeasuring system of FIGS. 1A-1C.

FIGS. 2A-2B show aspects of a technique for measuring displacements of abinary intensity pattern.

FIGS. 3A-3C show aspects of a technique for measuring displacements of abinary intensity pattern in a single-ended manner.

FIGS. 4A-4C show aspects of show aspects of another technique formeasuring displacements of a binary intensity pattern in a differentialmanner.

FIGS. 5A-5C show aspects of a differential measurement used by thedisplacement measuring system of FIGS. 1A-1C.

FIGS. 6A-6B show aspects of a technique for measuring displacements of abinary intensity pattern in a combined single-ended and differentialmanner.

FIGS. 7A-7C show aspects of an angular displacement measuring system.

FIGS. 8A-8B show aspects of a technique for measuring angulardisplacement used by the angular displacement measuring system of FIGS.7A-7C.

FIGS. 9A-9L show aspects of a displacement measuring system thatincludes an optical sensing system and a bEMF sensing system.

FIGS. 10A-10B show aspects of an example of an interpolator module usedby the displacement measuring system of FIGS. 9A-9L.

FIGS. 11A-11B show aspects of a haptic system that uses the displacementmeasuring system of FIGS. 9A-9L.

FIGS. 12A-12I show aspects of another optical sensing system to be usedin conjunction with the displacement measuring system of FIG. 9A.

FIGS. 13A-13C show examples of optical structures of the displacementmeasuring system of FIG. 9A that are used for redirecting probe lightthat illuminates an intensity pattern to a photodetector.

FIGS. 14A-14C show other examples of optical structures of thedisplacement measuring system of FIG. 9A that are used for redirectingprobe light that illuminates an intensity pattern to a photodetector.

FIG. 15A shows an example of displacement measuring system.

FIG. 15B shows another example of displacement measuring system.

FIG. 15C shows an example of a binary intensity pattern used to measure1D displacements.

FIGS. 15D-15F show aspects of operating displacement measuring systems.

FIGS. 16A-16B show aspects of determining location on the binaryintensity pattern of FIG. 15C.

FIG. 17A shows an example of a three-level intensity pattern used tomeasure 15D displacements.

FIGS. 17B-17C show aspects of determining location on the three-levelintensity pattern of FIG. 17A.

FIGS. 18A-18B show modifications to the displacement measuring system ofFIGS. 15A-15B.

FIG. 18C shows an example of a four-level intensity pattern used tomeasure 2D displacements.

FIGS. 18D-18E show aspects of determining location on the four-levelintensity pattern of FIG. 18C.

FIGS. 19A-19B show aspects of a technique for addressing misalignment ofintensity pattern relative to a light emitting element array.

FIGS. 20A-20B show aspects of an angular displacement measuring system.

FIGS. 21A-21B show aspects of another angular displacement measuringsystem.

FIGS. 22A-22B show aspects of another displacement measuring system.

Certain illustrative aspects of the systems, apparatuses, and methodsaccording to the disclosed technologies are described herein inconnection with the following description and the accompanying figures.These aspects are, however, indicative of but a few of the various waysin which the principles of the disclosed technologies may be employedand the disclosed technologies are intended to include all such aspectsand their equivalents. Other advantages and novel features of thedisclosed technologies may become apparent from the following detaileddescription when considered in conjunction with the figures.

DETAILED DESCRIPTION

FIG. 1A is a side view, e.g. in the (x,z) plane, of an example of adisplacement measuring system 100. The displacement measuring system 100includes a mount 104, a light source 106 supported by the mount, anoptical pattern 118 disposed on a surface 135XY of a mass 134 that isspaced apart from the light source, a photodetector 124 supported by themount, and processing electronics 125 coupled with the photodetector.

FIG. 1B is a plan view, e.g., in the (x,y) plane, of the optical pattern118. In this example, the optical pattern 118 has two portions 120, 122that form a rectangular edge 121 with sides parallel to correspondingx-axis and y-axis. The first portion 120 (shown in white) has a firstreflectivity R₁, and the second portion 122 (shown in grey) has a secondreflectivity R₂, smaller than the first reflectivity. For example, thesecond reflectivity R₂ can be at most half the first reflectivity R₁,e.g., R₂=0.3R₁, 0.1R₁, 0.05R₁ or other fractions of R₁. As lightimpinging on the first portion 120 reflects off it with a firstintensity, and light impinging on the second portion 122 reflects off itwith a second intensity smaller than the first intensity, the opticalpattern is also referred to as a binary intensity pattern 118. In someimplementations, the first portion 120 is coated with a reflective filmand the second portion 122 is coated with an absorptive film. In someimplementations, the first portion 120 is coated with a multilayerreflection coating and the second portion 122 is coated with amultilayer anti-reflection coating.

FIG. 1C is a plan view, e.g., in the (x,y) plane, of the components ofthe displacement measuring system 100 supported by the mount 104. Thelight source 106 can include one or more light emitting element (LEE)arrays 110. In the example illustrated in FIG. 1C, the light source 106includes LEE arrays 110A, 110B, 110C, 110D.

Each LEE array, e.g., LEE array 110A, includes a driving board 112 and aplurality of light emitting elements (LEEs) 114, such that the drivingboard concurrently powers the LEEs of the LEE array, during operation ofthe displacement measuring system 100. Note that the LEEs 114 of an LEEarray 110 can be arranged in one or more rows parallel to each other. Inthe example illustrated in FIG. 1C, each LEE array, e.g., LEE array110A, includes rows 116A, 116B of LEEs 114 distributed along the x-axis.The LEEs 114 in a row 116A or 116B are separated by a pitch X. Moreover,the rows 116A and 116B are separated from each other along the y-axis bya separation δY, and are staggered relative to each other along thex-axis by half the pitch A. Further, a total size (e.g., length) alongthe x-axis of an LEE array 110 sets an upper bound MAX ΔX for adisplacement along the x-axis that can be measured by the displacementmeasuring system 100. Furthermore, a total size (e.g., width) along they-axis of an LEE array 110 sets an upper bound MAX ΔY for a displacementalong the y-axis that can be measured by the displacement measuringsystem 100. Note that a range of translational motion for a mass 134disposed inside a haptic engine, as described below in connection withFIGS. 1E-1F, is less than 0.6 mm.

Each LEE 114 of the light source 106 is configured to output collimatedlight, such that the LEE illuminates the optical pattern 118 with a beam115 that forms a well-defined (e.g., top-hat or Gaussian) beam spot onthe optical pattern. In this manner, displacement measurements performedby the displacement measuring system 100 are insensitive to a separationZ-offset between the light source 106 and the optical pattern 118. Insome implementations, each LEE 114 includes a light emitting diode (LED)and a collimating optic (e.g., a lens, a compound parabolicconcentrator, etc.) optically coupled with the LED. Such an LED emitsun-collimated light (e.g., in accordance with a Lambertiandistribution), and the collimating optic collimates the emitted light toissue collimated light. In other implementations, each LEE 114 includesa vertical cavity surface emitting laser (VCSEL) that emits collimatedlight. In this manner, when the LEEs are VCSELs, Z-offset between thelight source 106 and the optical pattern 118 can be very short, e.g., inthe range of 0.1 mm to 0.5 mm. Moreover, as light emitted by the VCSELs114 can have wavelengths in a range from 700 nm to 1100 nm, the secondportion 122 of the optical pattern 118 can be printed using ink thatabsorbs IR light.

Additionally, each LEE array 110 is arranged relative to the opticalpattern 118 such that its LEEs 114 illuminate with collimated light,during operation of the displacement measuring system 100, the opticalpattern 118 across a corresponding corner of the rectangular edge 121,as explained below in this specification. The optical pattern 118redirects to the photodetector 124, e.g., via reflection or scattering,at least some of the collimated light 115 from an LEE array 110 thatimpinges on the optical pattern. The photodetector 124 captures theredirected light 119 associated with the LEE array 110 and integratesit. In some implementations, the photodetector 124 can be a CMOS sensorarray. In some implementations, the photodetector 124 can be a CCDsensor array.

Moreover, as a result of integrating the captured light, thephotodetector 124 issues a photodetector signal relating to thecollimated light output by an LEE array 110 that is redirected by theoptical pattern 118 to the photodetector. In the example shown in FIGS.1A and 1C, the photodetector 124 issues a respective photodetectorsignal relating to the collimated light output by a corresponding one ofthe LEE arrays 110A, 110B, 110C, 110D, where the issued photodetectorsignals are multiplexed based on a multiplexing scheme used toilluminate the optical pattern 118.

In some implementations, the LEEs 114 of the LEE arrays 110A, 110B,110C, 110D emit light of different wavelengths, λ_(A), λ_(B), λ_(C),λ_(D). In this case, the LEEs 114 of the LEE arrays 110A, 110B, 110C,110D illuminate the optical pattern 118 concurrently, using a wavelengthmultiplexing scheme. As such, the issued photodetector signals also arewavelength multiplexed. For example, the photodetector 124 can include aset of four sensors v₁, v₂, v₃, v₄, each sensor being covered with afilter of different cut-off wavelength to match the wavelengths λ_(A),λ_(B), λ_(C), λ_(D) of light emitted by the LEE arrays 110A, 110B, 110C,110D. And the signals corresponding to at least some of the wavelengthsλ_(A), λ_(B), λ_(C), λ_(D) of the emitted light can be isolated bycombining signals output by multiple of the sensors. For example, thefirst sensor, v₁, has a filter that passes wavelengths up to λ_(A) andoutputs a first sensor signal V₁, the second sensor, v₂, has a filterthat passes wavelengths up to λ_(B) and outputs a second sensor signalV₂, the third sensor, v₃, has a filter that passes wavelengths up toλ_(C) and outputs a third sensor signal V₃, and the fourth sensor, v₄,has a filter that passes wavelengths up to λ_(D) and outputs a fourthsensor signal V₄, where λ_(A)<λ_(B)<λ_(C)<λ_(D). Then a firstphotodetector signal in the band of λ_(A) can be isolated as V₁, asecond photodetector signal in the band of λ_(B) can be isolated as(V₂−V₁), a third photodetector signal in the band of can be isolated(V₃−V₂), and a fourth photodetector signal in the band of λ_(D) can beisolated as (V₄−V₃). As another example, the first sensor, v₁, has afilter that stops wavelengths up to λ_(A) and outputs a first sensorsignal V₁, the second sensor, v₂, has a filter that stops wavelengths upto λ_(B) and outputs a second sensor signal V₂, the third sensor, v₃,has a filter that stops wavelengths up to and outputs a third sensorsignal V₃, and the fourth sensor, v₄, has a filter that stopswavelengths up to λ_(D) and outputs a fourth sensor signal V₄, whereλ_(A)<λ_(B)<λ_(C)<λ_(D). Then a first photodetector signal in the bandof λ_(A) can be isolated as (V₁−V₂), a second photodetector signal inthe band of λ_(B) can be isolated as (V₂−V₃), a third photodetectorsignal in the band of λ_(C) can be isolated as (V₃−V₄), and a fourthphotodetector signal in the band of λ_(D) can be isolated as V₄.

In other implementations, the LEEs 114 of the LEE arrays 110A, 110B,110C, 110D emit light of the same wavelength. In this case, the LEEs 114of the LEE arrays 110A, 110B, 110C, 110D illuminate the optical pattern118 concurrently, using a time multiplexing scheme. FIG. 1D is anexample of a timing diagram used for time multiplexing the lightredirected by the optical pattern 118 to the photodetector 124. As such,light from the LEE array 110A that is redirected by the optical pattern118 reaches the photodetector 124 in accordance with timing gate 126A;light from the LEE array 110B that is redirected by the optical patternreaches the photodetector in accordance with timing gate 126B; lightfrom the LEE array 110C that is redirected by the optical patternreaches the photodetector in accordance with timing gate 126C; and lightfrom the LEE array 110D that is redirected by the optical patternreaches the photodetector in accordance with timing gate 126D. Note thatthe timing gates 126A, 126B, 126C, 126D are chosen such that light fromthe LEE array 110A that is redirected by the optical pattern 118 reachesthe photodetector 124 when light from the remaining LEE arrays 110B,110C, 110D is prevented from reaching the photodetector; light from theLEE array 110B that is redirected by the optical pattern 118 reaches thephotodetector when light from the remaining LEE arrays 110A, 110C, 110Dis prevented from reaching the photodetector; and so on. As such, thephotodetector 124 is said to operate in “shutter mode” because itreceives light from only one LEE array 110 at a time. For example, thephotodetector 124 can use a timing gate 128 that is synchronized withthe timing gates 126A, 126B, 126C, 126D to issue photodetector signalsthat are time multiplexed.

The processing electronics 125 receive one or more photodetector signalsissued by the photodetector 124 and determine displacements of the mass134 based on corresponding changes in the one or more photodetectorsignals caused by motion of the mass along, and orthogonal to, adirection of the rows 116 of LEEs 114 of the LEE arrays 110. Thespecific displacements that are determined by the processing electronics125 depend on positioning of the displacement measuring system 100inside a haptic engine 130 that includes the mass 134, as shown in FIGS.1E-1F. Note that the haptic engine 130 has a frame 132 that encompassesthe mass 134 and the displacement measuring system 100.

FIG. 1E is a side view, in the (y,z) plane, of the haptic engine 130, inwhich the optical pattern 118 of the displacement measuring system 100is supported by the mass 134 on a surface 135XY parallel to the (x,y)plane, and the mount 104 of the displacement measuring system issupported by the frame 132 on a face parallel to the (x,y) plane. Here,the rows 116 of LEEs 114 of the LEE arrays 110 are oriented along thex-axis. In this case, the processing electronics 125 determine adisplacement ΔX and a displacement ΔY of the mass 134 based oncorresponding changes in the one or more photodetector signals caused bymotion of the mass along the x-axis (e.g., vibration in-and-out of page)and motion of the mass along the y-axis (e.g., vibration left-right onpage).

FIG. 1F is a side view, in the (y,z) plane, of the haptic engine 130, inwhich the optical pattern 118 of the displacement measuring system 100is supported by the mass 134 on a surface 135XZ parallel to the (x,z)plane, and the mount 104 of the displacement measuring system issupported by the frame 132 on a face parallel to the (x,z) plane. Here,the rows 116 of LEEs 114 of the LEE arrays 110 are oriented along thex-axis. In this case, the processing electronics 125 determine adisplacement ΔX and a displacement ΔZ of the mass 134 based oncorresponding changes in the one or more photodetector signals caused bymotion of the mass along the x-axis (e.g., vibration in-and-out of page)and motion of the mass along the z-axis (e.g., vibration up-down onpage).

Prior to describing techniques for measuring displacements of the mass134 using the displacement measuring system 100, techniques for sensingmotion of an optical pattern that is illuminated by one or more beams isdescribed next.

FIG. 2A is a plan view, in the (x,y) plane, of a binary intensitypattern 218 that includes a first portion 220 corresponding to whitestrips and a second portion 222 corresponding to grey strips, where thestripes extend along the y-axis. A beam spot 236 shows a location wherea beam of collimated light (e.g., VCSEL light) illuminates the binaryintensity pattern 218. Note that in this example, a size of the beamspot 236 is about equal to a width of a strip along the x-axis. Here,the first portion 220 has a first reflectivity R₁, and the secondportion 222 has a second reflectivity R₂, smaller than the firstreflectivity. In this manner, as the binary intensity pattern 218 istranslated along the x-axis through the beam spot 236, the beam reflectsoff with a first intensity when it illuminates the first portion 220,and a second intensity, smaller than the first intensity, when itilluminates the second portion 222. A photodetector, to which thereflected beam is reflected, issues a photodetector signal 240proportional to the intensity of the reflected beam. Translation of thebinary intensity pattern 218 along the x-axis through the beam spot 236,causes changes of the photodetector signal 240. FIG. 2B shows changes ofthe photodetector signal 240 as a function of displacement ΔX of a datumof the binary intensity pattern 218 relative to the beam spot 236.

FIGS. 3A-3C show aspects relating to a displacement measurementtechnique that has a sensitivity free of dead-zones. FIG. 3A is a planview, in the (x,y) plane, of a binary intensity pattern 318 that has twoportions 320, 322 that form an edge 321 parallel to the y-axis. Aplurality of beam spots 336 show locations where respective beams ofcollimated light (e.g., VCSEL light) illuminate the binary intensitypattern 318. The beam spots 336 have equal sizes, so the associatedbeams that illuminate the binary intensity pattern 318 have the sameintensity. The first portion 320 (shown in white) has a firstreflectivity R₁, and the second portion 322 (shown in grey) has a secondreflectivity R₂, smaller than the first reflectivity. In this manner, abeam associated with a beam spot located on the first portion 320reflects off with a first intensity, and a beam associated with a beamspot located on the second portion 322 reflects off with a secondintensity, smaller than the first intensity.

Half of the beam spots 336 are arranged in a first row 338A and theother half of the beam spots are arranged in a second row 338B, wherethe rows 338A, 338B are parallel to each other and the x-axis. An in-rowpitch of the beam spots 336 within a row 338A or 338B is in a range of 1to 1.5 of a beam spot size. The rows 338A, 338B are staggered withrespect to each other along the x-axis by half the in-row pitch, and areseparated from each other along the y-axis by an inter-row pitch in arange of 0.8 to 1 of the beam spot size.

A first group of beams associated with the beam spots 336 of the firstrow 338A is referred to as a first macro-beam 338A, and a second groupof beams associated with the beam spots 336 of the second row 338B isreferred to as a second macro-beam 338B. Note that the macro-beams 338A,338B can be turned ON/OFF in a time multiplexed manner, i.e., when thefirst macro-beam 338A illuminates the binary intensity pattern 318, thesecond macro-beam 338B does not do so; and when the second macro-beam338B illuminates the binary intensity pattern 318, the first macro-beam338A does not do so. The binary intensity pattern 318 reflects the firstmacro-beam 338A (or second macro-beam 338B) to a photodetector. Thephotodetector captures the reflected first macro-beam 338A (or reflectedsecond macro-beam 338B), and integrates it. As a result of integratingthe captured light, the photodetector issues a first photodetectorsignal 342A (or second photodetector signal 342B) proportional to theintensity of the reflected first macro-beam 338A (or reflected secondmacro-beam 338B). In other words, the first photodetector signal 342A(or second photodetector signal 342B) is proportional to cumulativeintensity of the reflected beams of the first macro-beam 338A (or secondmacro-beam 338B).

Translation of the binary intensity pattern 318 along the x-axis throughthe first macro-beam 338A (or second macro-beam 338B), causes changes ofthe first photodetector signal 342A (or second photodetector signal342B). FIG. 3B shows changes of the first photodetector signal 342A (orsecond photodetector signal 342B) as a function of displacement ΔX ofthe edge 321 of the binary intensity pattern 318 relative to the firstmacro-beam 338A (or second macro-beam 338B). For instance, as beams ofthe first macro-beam 338A (or second macro-beam 338B) transition overthe edge 321, from the second portion 322 to the first portion 320, theintensity of the reflected first macro-beam 338A (or reflected secondmacro-beam 338B) increases, and so does the first photodetector signal342A (or second photodetector signal 342B), as shown in FIG. 3B. In thismanner, the maximum measurable displacement MAX ΔX of the edge 321 ofthe binary intensity pattern 318 relative to the first macro-beam 338A(or second macro-beam 338B) is substantially equal to the length of thefirst macro-beam 338A (or second macro-beam 338B) along the x-axis.

FIG. 3C shows a gradient 344A of the first photodetector signal 342A (orgradient 344B of the second photodetector signal 342B). Note that eachpeak/valley pair of the gradient 344A (or gradient 344B) corresponds toa crossing of the edge 321 through another beam of the first macro-beam338A (or second macro-beam 338B) as the binary intensity pattern 318 istranslated along the x-axis. The resolution of this displacementmeasurement is given by a spot size of beam spot 336. For instance, spotsize for a VCSEL beam can be less than 10 μm. By counting, from thegradient 344A of the first photodetector signal 342A (or gradient 344Bof the second photodetector signal 342B), the number of beam spotcrossings over the edge 321, one can determine an accurate value of theabsolute displacement ΔX. This can be used as an optical ruler tocalibrate absolute displacement for a known spot size of the beam spot336.

Note that dead-zones in the sensitivity of the foregoing displacementmeasurement occur when the edge 321 of the binary intensity pattern 318is between beams of the first macro-beam 338A (or second macro-beam338B), for values of the gradient 344A of the first photodetector signal342A (or gradient 344B of the second photodetector signal 342B) equal tozero (ΔI/ΔX=0). To avoid the foregoing dead-zones, the multiplexed firstphotodetector signal 342A and second photodetector signal 342B can becombined together, e.g., by averaging or interpolating them together, toobtain a smooth photodetector signal. The combining together of thefirst photodetector signal 342A and second photodetector signal 342B canbe can be accomplished by activating, at the same time, both the firstmacro-beam 338A and the second macro-beam 338B. In this manner, themeasurement of the displacement ΔX is performed using a singlemacro-beam 350 that includes both rows 338A and 338B of beams, asexplained below in this specification.

FIGS. 4A-4C show aspects relating to a differential sensing mode of adisplacement measurement technique. FIG. 4A is a plan view, in the (x,y)plane, of a binary intensity pattern 418 that has a first portion 420(shown in white) and a second portion 422 (shown in grey), the twoportions forming a first edge 421A and a second edge 421B that areparallel to each other and the y-axis. A plurality of beam spots 436show locations where respective beams of collimated light (e.g., VCSELlight) illuminate the binary intensity pattern 418. The beam spots 436have equal sizes, so the associated beams that illuminate the binaryintensity pattern 418 have the same intensity. The first portion 420 hasa first reflectivity R₁, and the second portion 422 has a secondreflectivity R₂, smaller than the first reflectivity. In this manner, abeam associated with a beam spot located on the first portion 420reflects off with a first intensity, and a beam associated with a beamspot located on the second portion 422 reflects off with a secondintensity, smaller than the first intensity.

A first group of beams associated with half of the beam spots 436 isreferred to as a first macro-beam 450A, and a second group of beamsassociated with the other half of the beam spots 436 is referred to as asecond macro-beam 450B. The beam spots 436 of the first macro-beam 450A(or second macro-beam 450B) are arranged in two rows 438A, 438B that areparallel to each other and the x-axis. An in-row pitch of the beam spots436 within a row 438A (or 438B) is in a range of 1 to 1.5 of a beam spotsize. The rows 438A, 438B are staggered with respect to each other alongthe x-axis by half the in-row pitch, and are separated from each otheralong the y-axis by an inter-row pitch in a range of 0.8 to 1 of thebeam spot size. A length of the macro-beams 450A, 450B along the x-axisis about equal to a separation between the first edge 421A and thesecond edge 421B of the binary intensity pattern 418. In this manner,for any displacement ΔX of the binary intensity pattern 418 relative tothe macro-beams 450A, 450B that is smaller than a maximum measurabledisplacement MAX ΔX, if the first macro-beam 450A illuminates the binaryintensity pattern across the first edge 421A, then the second macro-beam450B illuminates the binary intensity pattern across the second edge421B.

Note that the macro-beams 450A, 450B are turned ON/OFF in a timemultiplexed manner, i.e., when the first macro-beam 450A illuminates thebinary intensity pattern 418, the second macro-beam 450B does not do so;and when the second macro-beam 450B illuminates the binary intensitypattern 418, the first macro-beam 450A does not do so. The binaryintensity pattern 418 reflects the first macro-beam 450A and the secondmacro-beam 450B to a photodetector. The photodetector sequentiallycaptures (in a time multiplexed manner) the reflected first macro-beam450A and the reflected second macro-beam 450B, and separately integratesthem. As a result of integrating the captured light, the photodetectorissues a first photodetector signal 452A and a second photodetectorsignal 452B respectively proportional to the intensity of the reflectedfirst macro-beam 450A and the intensity of the reflected secondmacro-beam 450B. In other words, the first photodetector signal 452A isproportional to cumulative intensity of the reflected beams of the firstmacro-beam 450A, and the second photodetector signal 452B isproportional to cumulative intensity of the reflected beams of thesecond macro-beam 450B).

Translation of the binary intensity pattern 418 along the x-axis throughthe first macro-beam 450A and the second macro-beam 450B, causes changesof the first photodetector signal 452A and changes of the secondphotodetector signal 452B. FIG. 4B is a graph 451 which shows changes ofthe first photodetector signal 452A and changes of the secondphotodetector signal 452B as a function of displacement ΔX of a datum ofthe binary intensity pattern 418 relative to the first macro-beam 450Aand the second macro-beam 450B. The datum of the binary intensitypattern 418 can be either one of the first edge 421A or the second edge421B, for instance. Here, when the binary intensity pattern 418 istranslated from left-to-right on page, the following occurs: (1) Asbeams of the first macro-beam 450A transition over the first edge 421A,from the first portion 420 to the second portion 422, the intensity ofthe reflected first macro-beam 450A decreases, and so does the firstphotodetector signal 452A; and (2), as beams of the second macro-beam450B transition over the second edge 421B, from the second portion 422to the first portion 420, the intensity of the reflected secondmacro-beam 450B increases, and so does the second photodetector signal452B. Here, the first photodetector signal 452A and the secondphotodetector signal 452B have the same value, referred to as mid-pointintensity, at a mid-point displacement ΔX_(MP).

In this manner, displacement ΔX of the binary intensity pattern 418along the x-axis through the first macro-beam 450A and the secondmacro-beam 450B can be determined in a differential manner, as follows.A value of the first photodetector signal 452A and a value of the secondphotodetector signal 452B is measured for an unknown displacement ΔX. Adifference between the measured value of the first photodetector signal452A and the measured value of the second photodetector signal 452B isdetermined. Then, a value of the unknown displacement ΔX is uniquelyobtained by mapping the determined difference value onto graph 451. Notethat when the determined difference value is positive, the mapping isperformed for displacements that satisfy ΔX<ΔX_(MP), and when thedetermined difference value is negative, the mapping is performed fordisplacements that satisfy ΔX>ΔX_(MP). In some implementations, theforegoing differential displacement measurement can be performed by theprocessing electronics 125 of the displacement measuring system 100.

Note that the mid-point intensity value depends on a Z-offset between alight source (e.g., a portion of the light source 106 of thedisplacement measuring system 100) that provides the macro-beams 450A,450B and the binary intensity pattern 418 (e.g., the optical pattern 118of the displacement measuring system 100). For example, the mid-pointintensity value is large for a small Z-offset and small for a largeZ-offset. In this manner, displacements ΔZ along the z-axis of thebinary intensity pattern 418 relative the light source can be determinedbased on changes of the mid-point intensity value.

Sensitivities of the differential displacement measurement—describedabove in connection with FIG. 4B—due to drift in absolute lightintensity, caused by variations in temperature, Z-offset, VCSEL bias,etc., can be avoided by performing a displacement measurement in aratiometric mode. A first ratio signal 452A/452B is obtained by dividingthe first photodetector signal 452A to the second photodetector signal452B, and a second ratio signal 452B/452A is obtained by dividing thesecond photodetector signal 452B to the first photodetector signal 452A.FIG. 4C is a graph 453 which shows changes of the first ratio signal452A/452B and changes of the second ratio signal 452B/452A as a functionof displacement ΔX of the datum of the binary intensity pattern 418relative to the first macro-beam 450A and the second macro-beam 450B.Here, the first ratio signal 452A/452B and the first ratio signal452A/452B are both equal to one at a mid-point displacement ΔXMP, wherethe latter corresponding to the mid-point intensity.

Displacement ΔX of the binary intensity pattern 418 along the x-axisthrough the first macro-beam 450A and the second macro-beam 450B can bedetermined in a ratiometric manner, as follows. A value of the firstphotodetector signal 452A and a value of the second photodetector signal452B is measured for an unknown displacement ΔX. A first ratio of themeasured value of the first photodetector signal 452A to the measuredvalue of the second photodetector signal 452B, and a second ratio of themeasured value of the second photodetector signal 452B to the measuredvalue of the first photodetector signal 452A are obtained. A smaller ofthe obtained first ratio and second ratio is selected, and then, a valueof the unknown displacement ΔX is determined by mapping, in graph 453,the selected first ratio or second ratio onto the corresponding firstratio signal 452A/452B or second ratio signal 452B/452A. For the exampleillustrated in FIG. 4C, the obtained second ratio is smaller than theobtained first ratio, so the obtained second ratio is mapped, in graph453, onto the second ratio signal 452B/452A, for displacements thatsatisfy ΔX<ΔX_(MP). As another example, if the obtained first ratio weresmaller than the obtained second ratio, then the obtained first ratiowould be mapped, in graph 453, onto the first ratio signal 452A/452B,for displacements that satisfy ΔX>ΔX_(MP). Note that, by switchingbetween the first ratio signal 452A/452B and the second ratio signal452B/452A when the mid-point is crossed, divide-by-zero problem can beavoided. In other words, the second ratio signal 452B/452A is used fordetermining small displacements ΔX, and the first ratio signal 452A/452Bis used for sensing large displacements ΔX. In some implementations, theforegoing ratiometric displacement measurement can be performed by theprocessing electronics 125 of the displacement measuring system 100.

FIGS. 5A-5C are used to explain techniques for measuring displacementsof the mass 134 using the displacement measuring system 100 that wasdescribed above in connection with FIGS. 1A-1D. FIG. 5A is a plan view,in the (x,y) plane, of the optical pattern 118 described above inconnection with FIG. 1B. Note that the rectangular edge 121 of theoptical pattern 118 is formed from two edges 121XA, 121XB parallel tothe y-axis, and two edges 121YA, 121YB parallel to the x-axis. Aplurality of beam spots 136 show locations where respective beams ofcollimated light—output by LEEs 114 of light source 106—illuminate theoptical pattern 118. The beam spots 136 have equal sizes, so theassociated beams—output by LEEs 114 of light source 106—that illuminatethe optical pattern 118 have the same intensity.

A first group of beams—that form some of the beam spots 136 and areoutput by the LEEs 114 of the first LEE array 110A—is referred to as afirst macro-beam 150A, a second group of beams—that form some other ofthe beam spots 136 and are output by the LEEs of the second LEE array110B—is referred to as a second macro-beam 150B, a third group ofbeams—that form yet some other of the beam spots 136 and are output bythe LEEs of the third LEE array 110C—is referred to as a thirdmacro-beam 150C, and a fourth group of beams—that form yet some other ofthe beam spots 136 and are output by the LEEs of the fourth LEE array110D—is referred to as a fourth macro-beam 150D. The beam spots 136 ofthe first macro-beam 150A (or any other macro-beam 150B, 150C, 150D) arearranged in two rows 138A, 138B that are parallel to each other and thex-axis. The beams that form the beam spots 136 of the rows 138A, 138Brelating to any of the macro-beams 150A, 150B, 150C or 150D are outputby the LEEs 114 of the corresponding rows 116A, 166B.

An in-row pitch of the beam spots 136 within a row 138A (or 138B) is ina range of 1 to 1.5 of a beam spot size and is related to the pitch δXof the LEEs 114 within a row 116A (or 116B) of LEEs 114. The rows 138A,138B of beam spots 136 are staggered with respect to each other alongthe x-axis by half the in-row pitch, as are the rows 116A, 116B of LEEs114. Additionally, the rows 138A, 138B of beam spots 136 are separatedfrom each other along the y-axis by an inter-row pitch—in a range of 0.8to 1 of the beam spot size—that is related to the separation δY betweenthe rows 116A, 116B of LEEs 114.

A length of a macro-beam 150 along the x-axis—which relates to a lengthof a corresponding LEE array 110—is about equal to a separation betweenthe edges 121XA, 121XB that are parallel to the y-axis. In this manner,for any displacement ΔX of the optical pattern 118 relative to themacro-beams 150A, 150B, 150C or 150D that is smaller than a maximummeasurable displacement MAX ΔX, if the first macro-beam 150A (or thirdmacro-beam 150C) illuminates the optical pattern across the first edge121XA parallel to the y-axis, then the second macro-beam 150B (or fourthmacro-beam 150D) illuminates the binary intensity pattern across thesecond edge 121XB parallel to the y-axis. Additionally, a width of amacro-beam 150 along the y-axis—which relates to a width of acorresponding LEE array 110—is about equal to a separation between theedges 121YA, 121YB that are parallel to the x-axis. In this manner, forany displacement ΔY of the optical pattern 118 relative to themacro-beams 150A, 150B, 150C or 150D that is smaller than a maximummeasurable displacement MAX ΔY, if the first macro-beam 150A (or secondmacro-beam 150B) illuminates the optical pattern across the first edge121YA parallel to the x-axis, then the third macro-beam 150C (or fourthmacro-beam 150D) illuminates the binary intensity pattern across thesecond edge 121YB parallel to the x-axis.

Note that the macro-beams 150A, 150B, 150C, 150D are turned ON/OFF in atime multiplexed manner based on the timing gates 126A, 126B, 126C, 126Dshown in FIG. 1D. In this manner, when the first macro-beam 150Ailluminates the optical pattern 118, the macro-beams 150B, 150C, 150D donot do so; when the second macro-beam 150B illuminates the opticalpattern 118, the macro-beams 150A, 150C, 150D do not do so; and so on.The optical pattern 118 reflects the macro-beams 150A, 150B, 150C, 150Dto the photodetector 124. The photodetector 124 sequentially captures(in a time multiplexed manner based on the timing gate 128 shown in FIG.1D) the reflected macro-beams 150A, 150B, 150C, 150D, and separatelyintegrates them. As a result of integrating the captured light, thephotodetector 124 issues a first photodetector signal 552A, a secondphotodetector signal 552B, a third photodetector signal 552C and afourth photodetector signal 552D respectively proportional to theintensity of the reflected first macro-beam 150A, the intensity of thereflected second macro-beam 150B, the intensity of the reflected thirdmacro-beam 150C and the intensity of the reflected fourth macro-beam150D.

Translation of the optical pattern 118 along the x-axis through themacro-beams 150A, 150B, 150C, 150D, causes changes of the firstphotodetector signal 552A, changes of the second photodetector signal552B, changes of the third photodetector signal 552C and changes of thefourth photodetector signal 552D. FIG. 5B is a graph 551X which showschanges of the first photodetector signal 552A, changes of the secondphotodetector signal 552B, changes of the third photodetector signal552C and changes of the fourth photodetector signal 552D as a functionof displacement ΔX of a datum of the optical pattern 118 relative to themacro-beams 150A, 150B, 150C, 150D. The datum of the optical pattern 418can be either one of the corners of the rectangular edge 121, forinstance. Here, when the optical pattern 118 is translated fromleft-to-right on page without being translated up-or-down on page, thefollowing occurs: (1) As beams of the first macro-beam 150A and beams ofthe third macro-beam 150C transition over the first edge 121XA parallelto the x-axis, from the first portion 120 to the second portion 122, theintensity of each of the reflected first macro-beam 150A and thereflected third macro-beam 150C decreases, and so does each of therespective first photodetector signal 552A and the third photodetectorsignal 552C; and (2) as beams of the second macro-beam 150B and beams ofthe fourth macro-beam 150D transition over the second edge 121XBparallel to the y-axis, from the second portion 122 to the first portion120, the intensity of each of the reflected second macro-beam 150B andthe reflected fourth macro-beam 150D increases, and so does each of therespective second photodetector signal 552B and the fourth photodetectorsignal 552D.

As such, displacement ΔX of the optical pattern 118 along the x-axisthrough the macro-beams 150A, 150B, 150C, 150D can be determined in anyone or more of the following manners. For example, a differentialdisplacement measurement along the x-axis using (i) first photodetectorsignal 552A and (ii) second photodetector signal 552B can be performedsimilarly to the differential displacement measurement along the x-axisusing (i) the first photodetector signal 452A and (ii) the secondphotodetector signal 452B, as described above in connection with FIG.4B. As another example, a differential displacement measurement alongthe x-axis using (i) third photodetector signal 552C and (ii) fourthphotodetector signal 552D can be performed similarly to the differentialdisplacement measurement along the x-axis using (i) the firstphotodetector signal 452A and (ii) the second photodetector signal 452B,as described above in connection with FIG. 4B. As yet another example, adifferential displacement measurement along the x-axis using (i) acombination (e.g., an average, or interpolation) of first photodetectorsignal 552A and third photodetector signal 552C and (ii) a combination(e.g., an average, or interpolation) of second photodetector signal 552Band fourth photodetector signal 552D can be performed similarly to thedifferential displacement measurement along the x-axis using (i) thefirst photodetector signal 452A and (ii) the second photodetector signal452B, as described above in connection with FIG. 4B.

Moreover, translation of the optical pattern 118 along the y-axisthrough the macro-beams 150A, 150B, 150C, 150D, causes changes of thefirst photodetector signal 552A, changes of the second photodetectorsignal 552B, changes of the third photodetector signal 552C and changesof the fourth photodetector signal 552D. FIG. 5C is a graph 551Y whichshows changes of the first photodetector signal 552A, changes of thesecond photodetector signal 552B, changes of the third photodetectorsignal 552C and changes of the fourth photodetector signal 552D as afunction of displacement ΔY of the datum of the optical pattern 118relative to the macro-beams 150A, 150B, 150C, 150D. Here, when theoptical pattern 118 is translated from bottom-to-top on page withoutbeing translated left-or-right on page, the following occurs: (1) Asbeams of the first macro-beam 150A and beams of the second macro-beam150B transition over the first edge 121YA parallel to the x-axis, fromthe second portion 122 to the first portion 120, the intensity of eachof the reflected first macro-beam 150A and the reflected secondmacro-beam 150B increases, and so does each of the respective firstphotodetector signal 552A and the second photodetector signal 552B; and(2) as beams of the third macro-beam 150C and beams of the fourthmacro-beam 150D transition over the second edge 121YB parallel to thex-axis, from the first portion 120 to the second portion 122, theintensity of each of the reflected third macro-beam 150C and thereflected fourth macro-beam 150D decreases, and so does each of therespective third photodetector signal 552C and the fourth photodetectorsignal 552D. With the exception of aspect ratio, notice the symmetrybetween X and Y axes when comparing FIGS. 5B and 5C.

As such, displacement ΔY of the optical pattern 118 along the y-axisthrough the macro-beams 150A, 150B, 150C, 150D can be determined in anyone or more of the following manners. For example, a differentialdisplacement measurement along the y-axis using (i) first photodetectorsignal 552A and (ii) third photodetector signal 552C can be performedsimilarly to the differential displacement measurement along the x-axisusing (i) the first photodetector signal 452A and (ii) the secondphotodetector signal 452B, as described above in connection with FIG.4B. As another example, a differential displacement measurement alongthe y-axis using (i) second photodetector signal 552B and (ii) fourthphotodetector signal 552D can be performed similarly to the differentialdisplacement measurement along the x-axis using (i) the firstphotodetector signal 452A and (ii) the second photodetector signal 452B,as described above in connection with FIG. 4B. As yet another example, adifferential displacement measurement along the y-axis using (i) acombination (e.g., an average, or interpolation) of first photodetectorsignal 552A and second photodetector signal 552B and (ii) a combination(e.g., an average, or interpolation) of third photodetector signal 552Cand fourth photodetector signal 552D can be performed similarly to thedifferential displacement measurement along the x-axis using (i) thefirst photodetector signal 452A and (ii) the second photodetector signal452B, as described above in connection with FIG. 4B.

Note that, when the macro-beams 150A, 150B, 150C, 150D are concurrentlyoutput by the respective LEE arrays 110A, 110B, 110C, 110D of theoptical source 106, i.e., without using time multiplexing, then aphotodetector signal should have a constant value, regardless of whetherthe optical pattern 118 is at rest or it is translated in the (x,y)plane. As any deviation from this would be caused by irregularities(e.g., damage of, dust particles on, etc. a surface) of the opticalpattern 118, a self-health-check can be performed by translating theoptical pattern 118 over its full range of motion, e.g., MAX ΔX, whilethe LEE arrays 110A, 110B, 110C, 110D are activated concurrently.

Moreover, a saturation point of the intensity of the light reflected bythe optical pattern 118 depends on physical dimensions of the opticalpattern and of LEE arrays 110A, 110B, 110C, 110D. For example, thesaturation point (i.e., the maximum level of a photodetector signal) canbe determined for (i) a given geometry and size of the optical pattern118, (ii) a given geometry and size of the LEE arrays 110A, 110B, 110C,110D, (iii) a given arrangement of the optical pattern relative to theLEE arrays, e.g., Z-offset or another offset in the (x,y) plane, etc.Once determined, the saturation point can be used as a self-calibrationreference.

FIGS. 6A-6B show that when the area inside a haptic engine 130 and/orcost of the haptic engine is a restriction, the number of LEE arrays andan area of the optical pattern 118 can be halved if differential sensingis not needed in one of two directions. In the example shown in FIG. 6A,a modification of the displacement measuring system 100 includes LEEarrays 110A, 110B and an optical pattern 618A. The optical pattern 618Acorresponds to the top half of the optical pattern 118 described abovein connection with FIG. 1B and includes two portions 620A, 622A thatform an edge 621AY parallel to the x-axis and two edges 621AXA, 621AXBparallel to the y-axis. The first LEE array 110A provides a firstmacro-beam 650A that crosses the first edge 621AXA parallel to they-axis and the edge 621AY parallel to the x-axis; and the second LEEarray 110B provides a second macro-beam 650B that crosses the secondedge 621AXB parallel to the y-axis and the edge 621AY parallel to thex-axis. In this configuration, the modified displacement measuringsystem can be used to perform (i) a differential displacementmeasurement along the x-axis to accurately determine a value of adisplacement ΔX, and (ii) a single-ended displacement measurement alongthe y-axis to only determine whether there is motion along the y-axis.Here, the differential displacement measurement along the x-axis basedon the first macro-beam 650A transitioning over the first edge 621AXAparallel to the y-axis and the second macro-beam 650B transitioning overthe second edge 621AXB parallel to the y-axis is performed similarly tothe differential displacement measurement along the x-axis based on thefirst macro-beam 150A transitioning over the first edge 121XA parallelto the y-axis and the second macro-beam 150B transitioning over thesecond edge 121XB parallel to the y-axis, as described above inconnection with FIGS. 5A-5B. Additionally, the single-ended displacementmeasurement along the y-axis based on either the first macro-beam 650Aor the second macro-beam 650B or both transitioning over the edge 121AYis performed similarly to the single-ended displacement measurementalong the x-axis based on either the first macro-beam 338A or the secondmacro-beam 338B or both transitioning over the edge 321, as describedabove in connection with FIGS. 3A-3B.

In the example shown in FIG. 6B, another modification of thedisplacement measuring system 100 includes LEE arrays 110B, 110D and anoptical pattern 618B. The optical pattern 618B corresponds to the righthalf of the optical pattern 118 described above in connection with FIG.1B and includes two portions 620B, 622B that form an edge 621BX parallelto the y-axis and two edges 621BYA, 621BYB parallel to the x-axis. Thefirst LEE array 110B provides a first macro-beam 650B that crosses thefirst edge 621BYA parallel to the x-axis and the edge 621BX parallel tothe y-axis; and the second LEE array 110D provides a second macro-beam650D that crosses the second edge 621BYB parallel to the x-axis and theedge 621BX parallel to the y-axis. In this configuration, the modifieddisplacement measuring system can be used to perform (i) a differentialdisplacement measurement along the y-axis to accurately determine avalue of a displacement ΔY, and (ii) a single-ended displacementmeasurement along the x-axis to only determine whether there is motionalong the x-axis. Here, the differential displacement measurement alongthe y-axis based on the first macro-beam 650B transitioning over thefirst edge 621BYA parallel to the x-axis and the second macro-beam 650Dtransitioning over the second edge 621BYB parallel to the x-axis isperformed similarly to the differential displacement measurement alongthe y-axis based on the second macro-beam 150B transitioning over thefirst edge 121YA parallel to the x-axis and the fourth macro-beam 150Dtransitioning over the second edge 121YB parallel to the x-axis, asdescribed above in connection with FIG. 5A and FIG. 5C. Additionally,the single-ended displacement measurement along the x-axis based oneither the first macro-beam 650B or the second macro-beam 650D or bothtransitioning over the edge 121BX is performed similarly to thesingle-ended displacement measurement along the x-axis based on eitherthe first macro-beam 338A or the second macro-beam 338B or bothtransitioning over the edge 321, as described above in connection withFIGS. 3A-3B.

Additionally, the disclosed displacement measuring system 100 can befurther modified to also determine angular displacements. Such anangular displacement measuring system can be used in conjunction with acrown of a watch device (e.g., a setting wheel that functions as aswitch, as it translates sideways, and as a scroller, as it rotatesaround a center axis), a wheel of a pointing device, a rotating hingefor a screen of a laptop computer, etc.

FIG. 7A is a side view, e.g. in the (x,z) plane, of an example of anangular displacement measuring system 700. The angular displacementmeasuring system 700 includes a mount 704, a light source 706 supportedby the mount, an optical pattern 718 disposed on the edge (perimeter)surface of a wheel 734 such that optical pattern is spaced apart fromthe light source, a photodetector 724 supported by the mount, andprocessing electronics 725 coupled with the photodetector.

The optical pattern 718 wraps around the perimeter surface of the wheel734, as shown in FIG. 7B. In this example, the optical pattern 718 has abackground portion 722 (shown in grey) that wraps around the perimetersurface of the wheel 734, and multiple rectangular portions 720A, 720B,720C, etc. (shown in white) distributed around the perimeter surface ofthe wheel that form corresponding rectangular edges 721A, 721B, 721C,etc. Note that each rectangular edge 721 has two azimuthal sidesparallel to a direction of rotation θ, and two transverse sides acrossthe direction of rotation θ (i.e., parallel to the y-axis). Here, eachof the rectangular portions 720A, 720B, etc. has a first reflectivityR1, and the background portion 722 has a second reflectivity R2, smallerthan the first reflectivity. Moreover, in this example, a size of eachrectangular portion 720 along the direction of rotation θ issubstantially equal to a separation between adjacent rectangularportions.

In the above-noted uses of the angular displacement measuring system700, where a direction and magnitude of angular displacement is to bemeasured over multiple periods of the optical pattern 718, a 3-phasearchitecture can be used as described below. FIG. 7C is a plan view,e.g., in the (x,y) plane, of the components of the angular displacementmeasuring system 700 supported by the mount 704. In this example, thelight source 706 includes a first pair of LEE arrays 710A, 710B, asecond pair of LEE arrays 710C, 710D, a third pair of LEE arrays 710E,710F, and the photodetector 724. Each of the LEE arrays 710A, 710B,710C, 710D, 710E, 710F and the photodetector 724 can be implemented, asdescribed above in connection with FIG. 1C, as an LEE array 110 and asthe photodetector 124, respectively. The LEE arrays 710A, 710B, 710C,710D, 710E, 710F are configured to output light beams grouped inrespective macro-beams 850A, 850B, 850C, 850D, 850E, 850F, such that themacro-beams illuminate, during operation of the angular displacementmeasuring system 700, the optical pattern 718 across the rectangularedges 721A, 721B, 721C, etc., as shown in FIG. 8A. Note that in thisexample, a length of each macro-beam 850 is substantially equal to thesize of each rectangular portion 720 along the direction of rotation θ.Moreover, the LEE arrays 710A, 710B, 710C, 710D, 710E, 710F outputrespective macro-beams 850A, 850B, 850C, 850D, 850E, 850F in a timemultiplexed manner.

The optical pattern 718 reflects to the photodetector 724 the macro-beamoutput by each LEE array 710 that impinges on the optical pattern. Notethat in this example, the macro-beams 850B, 850E emitted by the secondpair of LEE arrays 710B, 710E are reflected to the photodetector 724 ina backward direction, such that a cross-section of the second pair ofreflected macro-beams 850B, 850E is parallel to the surface of thephotodetector 724. However, because of the curved configuration of theoptical pattern 718, the macro-beams 850A, 850D (or 850C, 850F) emittedby the first pair of LEE arrays 710A, 710D (or third pair of LEE arrays710A, 710D) are reflected to the photodetector 724 in a direction tiltedrelative to the backward direction, such that a cross-section of thefirst pair of reflected macro-beams 850A, 850D (or third pair ofreflected macro-beams 850C, 850F) form an angle of +120° (or −120°) tothe surface of the photodetector 724.

The photodetector 724 captures the reflected macro-beam 850 associatedwith each LEE array 710 and integrates it. As a result of integratingthe captured reflected macro-beam 850, the photodetector 724 issues, ina time multiplexed manner, a respective photodetector signal relating tothe associated macro-beam 850. Note that the processing circuitry 725can combine, e.g., average or interpolate together, the photodetectorsignals associated with the macro-beams of a pair of macro-beams todetermine a combined photodetector signal associated with that pair ofmacro-beams. As such, a first combined photodetector signal 856ADassociated with the first pair of macro-beams 850A, 850D is determinedby combining a first photodetector signal associated with the firstmacro-beam 850A together with a fourth photodetector signal associatedwith the fourth macro-beam 850D; a second combined photodetector signal856BE associated with the second pair of macro-beams 850B, 850E isdetermined by combining a second photodetector signal associated withthe second macro-beam 850B together with a fifth photodetector signalassociated with the fifth macro-beam 850E; and a third combinedphotodetector signal 856CF associated with the third pair of macro-beams850C, 850F is determined by combining a third photodetector signalassociated with the third macro-beam 850C together with a sixthphotodetector signal associated with the sixth macro-beam 850F.

Rotation of the of the optical pattern 718 along the direction ofrotation θ through the first pair of macro-beams 850A, 850D, the secondpair of macro-beams 850B, 850E, and the third pair of macro-beams 850C,850F, causes changes of the respective combined photodetector signals856AD, 856BE, 856CF. FIG. 8B is a graph 8510 which shows changes of thefirst combined photodetector signal 856AD, changes of the secondcombined photodetector signal 856BE, and changes of the third combinedphotodetector signal 856CF as a function of angular displacement Δθ of adatum of the optical pattern 718 relative to the first pair ofmacro-beams 850A, 850D, the second pair of macro-beams 850B, 850E, andthe third pair of macro-beams 850C, 850F. The datum of the opticalpattern 718 can be either one of the corners of either one of therectangular edges 721A, 721B, 721C, etc., for instance. Here, when theoptical pattern 718 is rotated from left-to-right on page without beingtranslated up-or-down on page, the following occurs: (1) As beams of thesecond pair of macro-beams 850B, 850E transition over the rectangularportions 720A, 720B, 720C, etc., the intensity of the reflected secondpair of macro-beams 850B, 850E forms corresponding peaks, and so doesthe second combined photodetector signal 856BE; at the same time, beamsof the first pair of macro-beams 850A, 850D and beams of the third pairof macro-beams 850C, 850F transition over the background portion 722between corresponding adjacent rectangular portions 720A, 720B, 720C,etc., so each of the intensity of the reflected first pair ofmacro-beams 850A, 850D and the intensity of the reflected third pair ofmacro-beams 850C, 850F forms corresponding valleys, and so does each ofthe first combined photodetector signal 856AD and the third combinedphotodetector signal 856CF; and (2) as beams of the second pair ofmacro-beams 850B, 850E transition over the background portion 722between adjacent rectangular portions 720A, 720B, 720C, etc., theintensity of the reflected second pair of macro-beams 850B, 850E formscorresponding valleys, and so does the second combined photodetectorsignal 856BE; at the same time, beams of the first pair of macro-beams850A, 850D and beams of the third pair of macro-beams 850C, 850Ftransition over the corresponding rectangular portions 720A, 720B, 720C,etc., so each of the intensity of the reflected first pair ofmacro-beams 850A, 850D and the intensity of the reflected third pair ofmacro-beams 850C, 850F forms corresponding peaks, and so does each ofthe first combined photodetector signal 856AD and the third combinedphotodetector signal 856CF.

In this manner, angular displacement Δθ of the optical pattern 718 alongthe direction of rotation θ through the first pair of macro-beams 850A,850D, the second pair of macro-beams 850B, 850E, and the third pair ofmacro-beams 850C, 850F can be determined in the following manner. Avalue of the first combined photodetector signal 856AD, a value of thesecond combined photodetector signal 856BE, and a value of the thirdcombined photodetector signal 856CF are measured for an unknowndisplacement ΔX. Then, a value of the unknown angular displacement Δθ isunambiguously obtained by mapping onto graph 451 the measured value ofthe first combined photodetector signal 856AD, the measured value of thesecond combined photodetector signal 856BE, and the measured value ofthe third combined photodetector signal 856CF.

Moreover, the angular displacement measuring system 700 can be used toperform a differential displacement measurement along the y-axis toaccurately determine a value of a displacement ΔY of the optical pattern718. Here, the differential displacement measurement along the y-axisbased on the second macro-beam 850B transitioning over a first azimuthalside of rectangular edges 721A, 721B, 721C, etc., and the fifthmacro-beam 650E transitioning over the second azimuthal side ofrectangular edges 721A, 721B, 721C, etc., is performed similarly to thedifferential displacement measurement along the y-axis based on eitherthe first macro-beam 150A or the second macro-beam 150B transitioningover the first edge 121YA parallel to the x-axis, and the respectivethird macro-beam 150C or fourth macro-beam 150D transitioning over thesecond edge 121YB parallel to the x-axis, as described above inconnection with FIG. 5A and FIG. 5C.

In some implementations, processing electronics 125 or 725 can beconfigured in analog electronics. Here, the analog electronics includeone or more filters, subtractors, dividers, comparators, and otheranalog electronics components for performing operations described inthis specification. In some implementations, processing electronics 125or 725 can be configured as mixed signal circuitry that processes analogsignals and digital signals. In some implementations, processingelectronics 125 or 725 can be configured as one or more digital signalprocessors, e.g., ASIC, FPGA, CPU, etc.

FIG. 9A is a side view, e.g. in the (x,z) plane, of an example of adisplacement measuring system 900 configured to measure displacement ofa mass 1164. Here, the displacement measuring system 900 includes anoptical sensing system 902, a back electromotive force (bEMF) sensingsystem 930 and a processor 925 coupled with both the optical sensingsystem and the bEMF sensing system.

In this example, the optical sensing system 902 includes a mount 904, alight source 906 supported by the mount, an intensity pattern 910disposed on a surface 1165XYA of the mass 1164 that is spaced apart fromthe light source, and a photodetector 920 supported by the mount andcoupled with the processing electronics 925. During operation of theoptical sensing system 902, the light source 906 illuminates theintensity pattern 910 with probe light 908, and the intensity patternredirects to the photodetector 920, e.g., via reflection or scattering,at least some of the light impinging thereon.

FIG. 9B is a plan view, e.g., in the (x,y) plane, of the intensitypattern 910 that includes a plurality of tiles 912 separated from eachother by corresponding tile borders 913. Note that each tile has a sizelarger than a beam spot 916 formed by the probe light 908 thatilluminates the intensity pattern 910. For instance, a size of each ofthe tiles 912 can be 1.1, 1.5, 2× of the size of the beam spot 916. Insome implementations, the light source 906 includes a VCSEL that emitscollimated probe light that is delivered to the intensity pattern 910 asa probe beam (also referenced as 908). In some implementations, thelight source 906 includes an LED and beam-shaping optics that areoptically coupled with the LED. In this case, the LED emitsun-collimated light, and the beam-shaping optics receive theun-collimated light and issue the probe light 908, either as a probebeam or at least as focused probe light. In this manner, in either theseimplementations, a size of the beam spot 916 can be 20 μm, 10 μm, orsmaller.

Moreover, each tile 912 of the intensity pattern 910 is configured toredirect to the photodetector 920 light having an intensity differentfrom an intensity of light redirected to the photodetector by any of itsadjacent tiles. In the example shown in FIG. 9B, the intensity pattern910 is a binary intensity pattern because each tile 912A (or 912B) hasonly two adjacent tiles 912B (or 912A) configured to redirect to thephotodetector 920 light having the same intensity. As such, the binaryintensity pattern 910 has tiles of first type 912A and tiles of secondtype 912B, where each tile of first type 912A forms respective tileborders 913 with two adjacent tiles of second type 912B, and each tileof second type 912B forms respective tile borders 913 with two adjacenttiles of first type 912A. A tile of first type 912A is configured suchthat, when the probe beam 908 illuminates it, the redirected light 918has a maximum intensity I_(MAX). Further, a tile of second type 912B isconfigured such that, when the probe beam 908 illuminates it, theredirected light 918 has a minimum intensity I_(MIN), whereI_(MIN)<I_(MAX). Here, the tile borders 913 are distributed at knownlocations relative to each other along the x-axis, so the binaryintensity pattern 910 of the optical sensing system 902 can be used aspart of the displacement measuring system 900 to measure displacement ΔXof the mass 1164 along the x-axis. An example of a four-level intensitypattern 1210 of the optical sensing system 902 that can be used as partof the displacement measuring system 900 to measure, as described belowin connection with FIGS. 12A-12I, displacement ΔX of the mass 1164 alongthe x-axis and displacement ΔY of the mass along the y-axis.

Referring again to FIG. 9A, the photodetector 920 captures theredirected light 918 associated with the light source 906 and integratesit. In some implementations, the photodetector 920 can be implemented asa photodiode, e.g., a PIN photodiode. A result of integrating thecaptured light is a raw intensity value I(t) relating to the intensityof the light redirected by the intensity pattern 910 to thephotodetector 920 at sampling time t. The photodetector 920 includes athreshold module that classifies the raw intensity value I(t) against athreshold value Th. In the example illustrated in FIG. 9C, the thresholdmodule of the photodetector 920 can set I(t)=I_(MIN) if I(t)≤Th, orI(t)=I_(MAX) if I(t)>Th. In some implementations, the threshold value Thcan be predetermined. In other implementations, the threshold value Thcan be updated adaptively. For instance, a statistic<I>_(S) of the lastK values of raw intensity that are smaller than the threshold value Th,and another statistic<I>_(L) of the last K values of raw intensity thatare larger than the threshold value Th can be used to reset thethreshold value to Th=(<I>_(L)−<I>_(S))/2. Here, K≥2 and thestatistic<I> can be an average, truncated average, median, maximum orminimum, for instance. In this manner, the photodetector 920 issues anintensity signal 922 that can have only two values {I_(MIN), I_(MAX)}and is related to the intensity of the light redirected by the intensitypattern 910 to the photodetector, as the intensity pattern carried bythe mass 1164 is displaced along the x-axis relative to the probe beam908.

FIG. 9C further shows changes in the intensity signal 922 caused bymultiple tile border crossings that occur as the intensity pattern 910carried by the mass 1164 is displaced along the x-axis relative to theprobe beam 908. A tile border crossing is said to occur when theintensity pattern 910 is displaced, along a direction of motion thatintersects the tile borders 913, such that a tile border 913, formedbetween a tile of first type 912A and a tile of second type 912B,crosses through the beam spot 916 associated with the static probe beam908. In this manner, the probe beam 908 illuminates the tile of firsttype 912A (or the tile of second type 912B) before the tile bordercrossing and illuminates the tile of second type 912B (or the tile offirst type 912A) after the tile border crossing, such that the tileborder crossing causes a predefined decrease “−ΔI” (or a predefinedincrease “+ΔI”) in the intensity of the redirected light 918 betweenI_(MAX) and I_(MIN). In the example illustrated in FIG. 9C, theintensity signal 922 indicates that (i) tile border crossings from atile of second type 912B to a tile of first type 912A have occurred attimes t₁ and t₃, where the tile border crossing times t₁, t₃ aredetermined as the times when the intensity signal increases by+ΔI=I_(MAX)−I_(MIN); and (ii) tile border crossings from a tile of firsttype 912A to a tile of second type 912B have occurred at times t₂ andt₄, where the tile border crossing times t₂, t₄ are determined as thetimes when the intensity signal decreases by −ΔI=−(I_(MAX)−I_(MIN)).Further in the example illustrated in FIG. 9C, the intensity signal 922indicates that the probe beam 906 has illuminated a tile of second type912B from the start time to time t₁, between times t₂ and t₃ and aftertime t₄ until the final time; and a tile of first type 912A betweentimes t₁ and t₂, and times t₃ and t₄.

However, the foregoing information that can be extracted from theintensity signal 922 shown in FIG. 9C is insufficient for uniquelydetermining the displacement ΔX of the intensity pattern 910 carried bythe mass 1164 along the x-axis relative to the probe beam 908. Forinstance, FIG. 9D shows only a few from among many possible scans 926 ofthe intensity pattern 910 carried by the mass 1164 along the x-axisrelative to the probe beam 908. Here, a tile border crossing 928 isrepresented by an arrow over the tile border that is being crossed. Alsonote that a tilt is used to represent the border crossings 928 in FIG.9D to suggest their sequence in time. Note that although each of thescans 926A, 926B, 926C, 926D includes four tile border crossings 928,the scans have different starting and ending points, span differentdisplacement ranges, as explained below.

For scan 926A, the beam spot 916 starts at X₃ corresponding to thecenter of the third tile of the intensity pattern 910 and ends back atX₃; at t₁, a first tile border crossing occurs from the third tile tothe fourth tile, and then the beam spot 916 reaches X₄ corresponding tothe center of the fourth tile; next at t₂, a second tile border crossingoccurs from the fourth tile to the third tile, and then the beam spot916 reaches X₃ again; next at t₃, a third tile border crossing occursfrom the third tile to the fourth tile, and then the beam spot 916reaches X₄ again; next at t₄, a fourth tile border crossing occurs fromthe fourth tile to the third tile, and then the beam spot 916 returnsback to X₃. Thus, the largest displacement ΔX of the intensity pattern910 relative to the probe beam 908 during scan 926A is of order (X₄−X₃),e.g., approximately the pitch of the intensity pattern. Here, the pitchof the intensity pattern 910 includes a tile of first type 912A and atile of second type 912B.

For scan 926B, the beam spot 916 starts at X₃ corresponding to thecenter of the third tile of the intensity pattern 910 and ends back atX₃; at t₁, a first tile border crossing occurs from the third tile tothe fourth tile, and then the beam spot 916 reaches X₄ corresponding tothe center of the fourth tile; next at t₂, a second tile border crossingoccurs from the fourth tile to the fifth tile, and then the beam spot916 reaches X₅ corresponding to the center of the fifth tile; next att₃, a third tile border crossing occurs from the fifth tile to thefourth tile, and then the beam spot 916 reaches X₄ again; next at t₄, afourth tile border crossing occurs from the fourth tile to the thirdtile, and then the beam spot 916 returns back to X₃. Thus, the largestdisplacement ΔX of the intensity pattern 910 relative to the probe beam908 during scan 926B is of order (X₅−X₃), e.g., approximately 1.5 timesthe pitch of the intensity pattern.

For scan 926C, the beam spot 916 starts at X₃ corresponding to thecenter of the third tile of the intensity pattern 910 and ends at X₁corresponding to the first tile of the intensity pattern; at t₁, a firsttile border crossing occurs from the third tile to the fourth tile, andthen the beam spot 916 reaches X₄ corresponding to the center of thefourth tile; next at t₂, a second tile border crossing occurs from thefourth tile to the third tile, and then the beam spot 916 reaches X₃again; next at t₃, a third tile border crossing occurs from the thirdtile to the second tile, and then the beam spot 916 reaches X₂corresponding to the center of the second tile; next at t₄, a fourthtile border crossing occurs from the second tile to the first tile, andthen the beam spot 916 ends up at X₁ corresponding to the center of thefirst tile. Thus, the largest displacement ΔX of the intensity pattern910 relative to the probe beam 908 during scan 926C is of order (X₁−X₄),e.g., approximately twice the pitch of the intensity pattern.

For scan 926D, the beam spot 916 starts at X₁ corresponding to thecenter of the first tile of the intensity pattern 910 and ends at X₅corresponding to the center of the fifth tile of the intensity pattern;at t₁, a first tile border crossing occurs from the first tile to thesecond tile, and then the beam spot 916 reaches X₂ corresponding to thecenter of the second tile; next at t₂, a second tile border crossingoccurs from the second tile to the third tile, and then the beam spot916 reaches X₃ corresponding to the center of the third tile; next att₃, a third tile border crossing occurs from the third tile to thefourth tile, and then the beam spot 916 reaches X₄ corresponding to thecenter of the fourth tile; next at t₄, a fourth tile border crossingoccurs from the fourth tile to the fifth tile, and then the beam spot916 ends up at X₅. Thus, the largest displacement ΔX of the intensitypattern 910 relative to the probe beam 908 during scan 926D is of order(X₅−X₁), e.g., 2.5 times the pitch of the intensity pattern.

In order to determine, e.g., from among the scans 926A, 926B, 926C, 926Dshown in FIG. 9D, the actual scan used by the optical sensing system 902to acquire the intensity signal 922 shown in FIG. 9C, the processor 925has to spatially resolve the tile border crossings indicated by theintensity signal. A tile border crossing is said to be spatiallyresolved when the processor 925 specifies both the tile border at whichthe tile border crossing has occurred, and the direction in which thetile border crossing has occurred. In order to spatially resolve thetile border crossings indicated by the intensity signal 922, theprocessor 925 uses additional information provided by the bEMF sensingsystem 930. Note that in the example shown in FIG. 9A, the bEMF sensingsystem 930 includes a board 932, a coil 934 supported by the board, anda magnet 936 disposed on a surface 1165XYB of the mass 1164 opposite thesurface 1165XYA on which the intensity pattern 910 is disposed. Anoutput port 938 of the bEMF sensing system 930 is coupled internallywith the coil 934 and externally with the processor 925. The magnet 936is arranged relative to the coil 934 to interact with it when the magnetmoves along with mass 1164 relative to the coil. In the example shown inFIG. 9A, the coil 934 is at rest relative to a datum of the displacementmeasuring system 900 (e.g., a position of the probe beam 908) and thelongitudinal axis of the coil is parallel to the x-axis, as the magnet936 can move inside the coil along the longitudinal axis of the coil.

In this manner, a bEMF signal v(t) 923 is induced in the coil 934 whenthe magnet 936 is displaced along the x-axis together with the mass1164. A value of the bEMF signal v(t) 923 is proportional to a magnitudeof a velocity of the mass 1164 along the x-axis, such that if the valueof the bEMF signal is zero, then the mass it at rest; also, if the bEMFsignal v(t) 923 increases (or decreases), then the velocity of the massincreases (or decreases). Moreover, a sign of the bEMF signal v(t) 923indicates a direction along the x-axis of the velocity of the mass 1164,and, thus, a direction of the displacement ΔX. For example, if a valueof the bEMF signal v(t) 923 is positive (or negative), then the mass isdisplaced forward (or backward) along the x-axis. Moreover, the bEMFsensing system 930 includes an integrator module that integrates overtime the bEMF signal v(t) 923 induced in the coil 934 and obtains afirst displacement signal ΔX_(bEMF)(t) 940 associated with thedisplacement ΔX. In this manner, given reasonable analog-to-digital(ADC) resolution, the bEMF sensing system 930 issues, at its output port938, with good differential resolution, the first displacement signalΔX_(bEMF)(t) 940 associated with the displacement ΔX of the mass 1164that has been acquired concurrently with the intensity signal 922. Inthis manner, the processor 925 can extract additional information fromthe first displacement signal ΔX_(bEMF)(t) 940 acquired by the bEMFsensing system 930, and will use the extracted information to spatiallyresolve the tile border crossings indicated by the intensity signal 922,as described below.

FIG. 9E shows a first example of a bEMF signal v(t) 923A induced in thecoil 934 of the bEMF sensing system 930 over the same time duration whenthe intensity signal 922 shown in FIG. 9C was acquired by the opticalsensing system 902. Note that in this case, the bEMF signal v(t) 923Aindicates that the mass 1164 to which the magnet 936 is attached startsits motion at rest, then it moves in the positive direction of thex-axis over a first time interval T₁ until it comes to a first stop,then it moves in the negative direction of the x-axis over a second timeinterval T₂ until it comes to a second stop, then it moves again in thepositive direction of the x-axis over a third time interval T₃ until itcomes to a third stop, and then it moves again in the negative directionof the x-axis over a fourth time interval T₄ until it comes to a fourthand final stop. FIG. 9G shows a first displacement signal ΔX_(bEMF)(t)940A obtained by the bEMF sensing system 930 by integrating the bEMFsignal v(t) 923A shown in FIG. 9E. Note that in this first case, thefirst displacement signal ΔX_(bEMF)(t) 940A indicates that the mass 1164is displaced forward from about X₃ (e.g., the center of the third tile)to about X₄ (e.g., the center of the fourth tile) over the first timeinterval T₁ and third time interval T₃, and backward from about X₄ toabout X₃ over the second time interval T₂ and fourth time interval T₄.

At this point, the processor 925 can combine information extracted fromthe intensity signal 922 shown in FIG. 9C with information extractedfrom the bEMF signal v(t) 923A shown in FIG. 9E and with informationextracted from the first displacement signal ΔX_(bEMF)(t) 940A shown inFIG. 9F to obtain a second displacement signal ΔX_(OPT)(t) 942A shown inFIG. 9G, in the following manner. The processor 925 uses the intensitysignal 922 to determine the respective times t₁, t₂, t₃, t₄ when tileborder crossings have occurred, as explained above in connection withFIG. 9C. Further, the processor 925 uses the bEMF signal v(t) 923A todetermine that, at t₁, the first tile border crossing occurs in theforward x-axis direction because, during the first time interval T₁which includes t₁, the mass moves in the forward x-axis direction, asexplained above in connection with FIG. 9E; at t₂, the second tileborder crossing occurs in the backward x-axis direction because, duringthe second time interval T₂ which includes t₂, the mass moves in thebackward x-axis direction; at t₃, the third tile border crossing occursin the forward x-axis direction because, during the third time intervalT₃ which includes t₃, the mass moves in the forward x-axis direction;and at t₄, the fourth tile border crossing occurs in the backward x-axisdirection because, during the fourth time interval T₄ which includes t₄,the mass moves in the backward x-axis direction. As the foregoing tileborder crossings alternate in direction, they must correspond tocrossings of a single tile border. Furthermore, the first displacementsignal ΔX_(bEMF)(t) 940A is used to determine that the single tileborder that is crossed back and forth is the tile border 913(3,4) whichseparates the third tile and the fourth tile, because the mass movesback and forth along the x-axis direction between the third tile and thefourth tile, as explained above in connection with FIG. 9F. Note thatthe second displacement signal ΔX_(OPT)(t) 942A obtained in this manneris represented in FIG. 9G by filled diamonds with arrows. In this case,all the samples of the second displacement signal ΔX_(OPT)(t) 942A areplotted at a coordinate corresponding to the precise location of thetile border 913(3,4), and direction of the respective arrows correspondsto the direction of the tile border crossings at respective times t₁,t₂, t₃, t₄. Further note that the signals shown in FIGS. 9E, 9F and 9Gcorrespond to scan 926A shown in FIG. 9D.

FIG. 9I shows a second example of a bEMF signal v(t) 923B induced in thecoil 934 of the bEMF sensing system 930 over the same time duration whenthe intensity signal 922 shown in FIG. 9C was acquired by the opticalsensing system 902. Note that in this case, the bEMF signal v(t) 923Bindicates that the mass 1164 to which the magnet 936 is attached startsits motion at rest, then it moves in the positive direction of thex-axis over a first time interval T₁ until it comes to a first stop,then it moves in the negative direction of the x-axis over a second timeinterval T₂ until it comes to a second and final stop. FIG. 9J shows afirst displacement signal ΔX_(bEMF)(t) 940B obtained by the bEMF sensingsystem 930 by integrating the bEMF signal v(t) 923B shown in FIG. 9I.Note that in this second case, the first displacement signalΔX_(bEMF)(t) 940B indicates that the mass 1164 is displaced forward fromabout X₃ (e.g., the center of the third tile) through X₄ (e.g., thecenter of the fourth tile) to about X₅ (e.g., the center of the fifthtile) over the first time interval T₁, and backward from about X₅ toabout X₃ over the second time interval T₂.

At this point, the processor 925 can combine (i) information extractedfrom the intensity signal 922 shown in FIG. 9C with (ii) informationextracted from the bEMF signal v(t) 923B shown in FIG. 9I and with (iii)information extracted from the first displacement signal ΔX_(bEMF)(t)940B shown in FIG. 9J to obtain a second displacement signal ΔX_(OPT)(t)942B shown in FIG. 9K, in the following manner. The processor 925 usesthe intensity signal 922 to determine the respective times t₁, t₂, t₃,t₄ when tile border crossings have occurred, as explained above inconnection with FIG. 9C. Further, the processor 925 uses the bEMF signalv(t) 923B to determine that, at t₁ and at t₂, the first tile bordercrossing and the second tile border crossing respectively occur in theforward x-axis direction because, during the first time interval T₁which includes both t₁ and t₂, the mass moves in the forward x-axisdirection, as explained above in connection with FIG. 9E; and at t₃ andt₄, the third tile border crossing and the fourth tile border crossingrespectively occur in the backward x-axis direction because, during thesecond time interval T₂ which includes both t₃ and t₄, the mass moves inthe backward x-axis direction. As the first two of the foregoing tileborder crossings have the same forward direction, they must correspondto respective crossings in the forward direction of both tile borders ofa single tile, and as the last two of the foregoing tile bordercrossings have the same backward direction, they must correspond torespective crossings in the backward direction of both tile borders ofthe same tile. Furthermore, the first displacement signal ΔX_(bEMF)(t)940B is used to determine that the single tile that is crossed back andforth is the fourth tile having the center at X₄ and sharing tile border913(3,4) with the third tile and tile border 913(4,5) with the fifthtile, because the mass moves back and forth along the x-axis directionbetween the third tile and the fifth tile, as explained above inconnection with FIG. 9J. Note that the second displacement signalΔX_(OPT)(t) 942B obtained in this manner is represented in FIG. 9K byfilled diamonds with arrows. In this case, a first sample of the seconddisplacement signal ΔX_(OPT)(t) 942B is plotted at a coordinatecorresponding to a location of a first tile border 913(3,4) of thefourth tile, and a second sample of the second displacement signalΔX_(OPT)(t) 942B is plotted at a coordinate corresponding to a locationof a second tile border 913(4,5) of the fourth tile, and the forwarddirection of each of the arrows of the first two samples corresponds tothe forward direction of the tile border crossings at respective timest₁, t₂. Further in this case, a third sample of the second displacementsignal ΔX_(OPT)(t) 942B is plotted at the coordinate corresponding tothe location of the second tile border 913(4,5) of the fourth tile, anda fourth sample of the second displacement signal ΔX_(OPT)(t) 942A isplotted at the coordinate corresponding to the location of the firsttile border 913(3,4) of the fourth tile, and the backward direction ofeach of the arrows of the last two samples corresponds to the backwarddirection of the tile border crossings at respective times t₃, t₄. Notethat the signals shown in FIGS. 9I, 9J and 9K correspond to scan 926Bshown in FIG. 9D.

Moreover, the second displacement signal ΔX_(OPT)(t) 942A (or 942B)determined based in part on the intensity signal 922 acquired by theoptical sensing system 902 has more absolute accuracy than the firstdisplacement signal ΔX_(bEMF)(t) 940A (or 940B) acquired by the bEMFsensing system 930, because the optical sensing system providesintegrated non-linearity (INL) that is lower than the INL of the bEMFsensing system. However, note that as the tile borders 913 aredistributed at known locations relative to each other along the x-axis,the spatial resolution of second displacement signal ΔX_(OPT)(t) 942A(or 942B) is limited by a photomask lithography process. Hence, thefirst displacement signal ΔX_(bEMF)(t) 940A (or 940B) acquired by thebEMF sensing system 930, as shown in FIG. 9F (or FIG. 9J) may beavailable at a larger sampling rate than the sampling rate used by theprocessor 925 to determine the second displacement signal ΔX_(OPT)(t)942A (or 942B), as shown in FIG. 9G (or FIG. 9K). As such, the processor925 can further determine a displacement signal ΔX(t) 944A (or 944B) byinterpolating the second displacement signal ΔX_(OPT)(t) 942A (or 942B)with appropriately scaled sampling values of the first displacementsignal ΔX_(bEMF)(t) 940A (or 940B). FIG. 9H shows a displacement signalΔX(t) 944A determined by the processor 925 by interpolating the seconddisplacement signal ΔX_(OPT)(t) 942A with appropriately scaled samplingvalues of the first displacement signal ΔX_(bEMF)(t) 940A. And FIG. 9Lshows a displacement signal ΔX(t) 944B determined by the processor 925by interpolating the second displacement signal ΔX_(OPT)(t) 942B withappropriately scaled sampling values of the first displacement signalΔX_(bEMF)(t) 940B.

FIG. 10A shows an example of an interpolator module 1045 forinterpolating the second displacement signal ΔX_(OPT)(t) 942 (examplesof which are shown in either of FIG. 9G or 9K) using the firstdisplacement signal ΔX_(bEMF)(t) 940 (examples of which are shown ineither of FIG. 9F or 9J) to obtain a displacement signal ΔX(t) 944(examples of which are shown in FIG. 9H or 9L). A digitized version ofthe first displacement signal ΔX_(bEMF)(t) 940 acquired by the bEMFsensing system 930 can be stored in a first buffer 1046; here, samplesof the first displacement signal ΔX_(bEMF)(t) 940 are denoted b[n] andare sampled at a first sampling rate. The second displacement signalΔX_(OPT)(t) 942, determined by the processor 925 based at least on theintensity signal 922 acquired by the optical sensing system 902, can bestored in a second buffer 1048; here, samples of the second displacementsignal ΔX_(OPT)(t) 942 are denoted p[m] and are sampled at a secondsampling rate that can be smaller than the first sampling rate. Thedisplacement signal ΔX(t) 944, obtained by the interpolator module 1045,can be stored in a third buffer 1059; here, samples of the displacementsignal ΔX(t) 944 are sampled at the first sampling rate. FIG. 10B showsa portion of a displacement signal ΔX(t) 944 obtained, as describedbelow, by the interpolator module 1045 and stored in the third buffer1059.

The interpolator module 1045 includes a subtractor 1050 linked to boththe first and second buffers 1046, 1048, and a differentiator 1055linked to the first buffer 1046. The interpolator module 1045 furtherincludes a divider 1052 linked to the subtractor 1050, and a filter 1054linked to the divider. Furthermore, the interpolator module 1045includes a multiplier 1056 linked to both the differentiator 1055 andthe filter 1054. Also, the interpolator module 1045 includes an adder1051 linked to the second buffer 1048. Additionally, the interpolatormodule 1045 includes a multiplexer 1058 linked to the second buffer1048, and an accumulator 1057 linked to both the multiplier 1056 and themultiplexer.

The interpolator module 1045 receives a sample p[m] of the seconddisplacement signal ΔX_(OPT)(t) 942 from the second buffer 1048 andpasses it through to the multiplexer 1058 to be output as anon-interpolated term p[m] of the displacement signal ΔX(t) 944 to thethird buffer 1059. Then, the multiplexer 1058 is switched to output ksequential interpolated terms of the displacement signal ΔX(t) 944,where k≥2, that are obtained in the following manner.

Prior to calculating the k interpolated terms, the subtractor 1050determines a change b[n]−b[n−k] of the first displacement signalΔX_(bEMF)(t) 940 over k of its samples and a change p[m]−p[m−j] of thesecond displacement signal ΔX_(OPT)(t) 942 over j of its samples, wherej≥1, and the divider 1052 determines a scale factor C as a ratio of theforegoing changes. In some implementations, the filter 1054 filters thescale factor C and outputs a filtered scale factor C to increasestability of the interpolation. Also prior to calculating the kinterpolated terms, the accumulator 1057 is initialized to zero.

To calculate the first interpolated term, the differentiator 1055outputs a first change (b[n+1]−b[n]) of the first displacement signalΔX_(bEMF)(t) 940. The multiplier 1056 scales the first change output bythe differentiator 1055 to obtain C(b[n+1]−b[n]). As the accumulator1057 has been initialized to zero, the first scaled changeC(b[n+1]−b[n]) is simply passed through the accumulator to the adder1051. The adder 1051 adds the first output of the accumulator 1057 tothe sample p[m] of the second displacement signal ΔX_(OPT)(t) 942, sothe interpolator module 1045 can use the multiplexer 1058 to output thefirst interpolated term p[m]+C(b[n+1]−b[n]) to the third buffer 1059. Tocalculate the second interpolated term, the differentiator 1055 outputsa second change (b[n+2]−b[n+1]) of the first displacement signalΔX_(bEMF)(t) 940. The multiplier 1056 scales the second change output bythe differentiator 1055 to obtain C(b[n+2]−b[n+1]). As the accumulator1057 has held the first scaled change C(b[n+1]−b[n]), the accumulationthereof with the second scaled change C(b[n+2]−b[n+1]) results inC(b[n+2]−b[n]) which is output to the adder 1051. The adder 1051 addsthe second output of the accumulator 1057 to the sample p[m] of thesecond displacement signal ΔX_(OPT)(t) 942, so the interpolator module1045 can use the multiplexer 1058 to output the second interpolated termp[m]+C(b[n+2]−b[n]) to the third buffer 1059. And so, and so forth, suchthat the k^(th) interpolated term output by the interpolator module 1045to the third buffer 1059 is p[m]+C(b[n+k−1]−b[n]).

Then, the multiplexer 1058 is switched to output the nextnon-interpolated term. Here, the interpolator module 1045 receives asample p[m+1] of the second displacement signal ΔX_(OPT)(t) 942 from thesecond buffer 1048 and passes it through to the multiplexer 1058 to beoutput as the next non-interpolated term p[m+1] of the displacementsignal ΔX(t) 944 to the third buffer 1059. The foregoing operations arethen iterated as necessary. Note that a portion of a displacement signalΔX(t) 944, that has been obtained as described above, is plotted FIG.10B.

Moreover, background calibration of the interpolator module 1045 can beperformed by using the intensity pattern 910 as absolute displacement ΔXreference, as described below. For instance, the filter 1054 canconditionally update the scale factor C after a change p[m]−p[m−j] ofthe second displacement signal ΔX_(OPT)(t) 942 over j of its samplesexceeds a certain displacement threshold. Setting a larger threshold(e.g., integrating over multiple tile border crossings) will improvecalibration accuracy, especially if the second sampling rate of thesecond displacement signal ΔX_(OPT)(t) 942 is low, but it would alsoreduce the update rate of the background calibration. In practice, thetemperature coefficient of the coil 934 used to acquire the firstdisplacement signal ΔX_(bEMF)(t) 942 is on the order of seconds, while amotion frequency of the mass 1164 inside a haptic engine is usually >50Hz, so calibration rate is not expected to be a problem.

Note that the displacement signal ΔX(t) 944 determined by the processor925, when the displacement measuring system 900 is arranged relative themoving mass 1164 as shown in FIG. 9A, is indicative of displacements ΔXof the mass along the x-axis. Other displacements can be determined bythe processor 925 depending on positioning of the displacement measuringsystem 900 inside a haptic engine that includes the mass 1164, or byusing extended capability of the displacement measuring system. FIGS.11A-11B show example implementations of a haptic engine 1160. In each ofthese implementations the haptic engine 1160 has a frame 1162 thatencompasses the mass 1164 and the displacement measuring system 900.

FIG. 11A is a side view, in the (y,z) plane, of a first implementationof the haptic engine 1160. Here, the optical sensing system 902 of thedisplacement measuring system 900 is arranged such that the intensitypattern 910 is supported by the mass 1164 on a surface 1165XYA parallelto the (x,y) plane, and the mount 904 is supported by the frame 1162 ona face parallel to the (x,y) plane. Here, the tile borders 913 of theintensity pattern 910 are oriented along the y-axis. Additionally, thebEMF sensing system 930 of the displacement measuring system 900 isarranged such that the magnet 936 is coupled with the mass 1164 at asurface 1165XYB parallel to the (x,y) plane and opposite to the surface1165XYA, and the coil 934 is coupled with the frame 1162 at another faceparallel to the (x,y) plane. Alternatively, the bEMF sensing system 930can be arranged such that the magnet 936 is coupled with the mass 1164at the same surface 1165XYA on which the intensity pattern 910 issupported, and the coil 934 is coupled with the frame 1162 at the sameface on which the mount 904 is supported. In either of thesearrangements, the longitudinal axis of the coil 934 is oriented parallelto the x-axis. In this first implementation of the haptic engine 1160,the processor 925 determines a displacement ΔX of the mass 1164 based oncorresponding changes in the first displacement signal ΔX_(bEMF)(t) 942and the second displacement signal ΔX_(OPT)(t) 942 caused by motion ofthe mass along the x-axis (e.g., vibration in-and-out of page). In otherimplementations, two instances of the bEMF sensing system 930 can beused in conjunction with one instance of the optical sensing system 902.For instance, a first instance of the bEMF sensing system 930 can bearranged on surface 1165XYA and a second instance of the bEMF sensingsystem 930 can be arranged on surface 1165XYB.

FIG. 11B is a side view, in the (y,z) plane, of a second implementationof the haptic engine 1160. Here, the optical sensing system 902 of thedisplacement measuring system 900 is arranged such that the intensitypattern 910 is supported by the mass 1164 on a surface 1165XZA parallelto the (x,z) plane, and the mount 904 is supported by the frame 1162 ona face parallel to the (x,z) plane. Here, the tile borders 913 of theintensity pattern 910 are oriented along the x-axis. Additionally, thebEMF sensing system 930 of the displacement measuring system 900 isarranged such that the magnet 936 is coupled with the mass 1164 at asurface 1165XZB parallel to the (x,z) plane and opposite to the surface1165XZA, and the coil 934 is coupled with the frame 1162 at another faceparallel to the (x,z) plane. Alternatively, the bEMF sensing system 930can be arranged such that the magnet 936 is coupled with the mass 1164at the same surface 1165XZA on which the intensity pattern 910 issupported, and the coil 934 is coupled with the frame 1162 at the sameface on which the mount 904 is supported. In either of thesearrangements, the longitudinal axis of the coil 934 is oriented parallelto the z-axis. In this second implementation of the haptic engine 1160,the processor 925 determines a displacement ΔZ of the mass 1164 based oncorresponding changes in the first displacement signal ΔX_(bEMF)(t) 942and the second displacement signal ΔX_(OPT)(t) 942 caused by motion ofthe mass along the z-axis (e.g., vibration up-and-down on page). Inother implementations, two instances of the bEMF sensing system 930 canbe used in conjunction with one instance of the optical sensing system902. For instance, a first instance of the bEMF sensing system 930 canbe arranged on surface 1165XZA and a second instance of the bEMF sensingsystem 930 can be arranged on surface 1165XZB.

In order to also measure a displacement ΔY of the mass 1164 along they-axis, e.g., corresponding to vibration left-and-right on page,concurrently with the displacement ΔX of the mass caused along thex-axis, e.g., corresponding to vibration in-and-out of page, anadditional instance of the displacement measuring system 900 can bedisposed adjacent to the instance of the displacement measuring system900 shown in FIG. 11A, for instance. In this case, the additionalinstance of the displacement measuring system 900 is arranged to have(i) the tile borders 913 of the intensity pattern 910 oriented along thex-axis, and (ii) the longitudinal axis of the coil 934 oriented parallelto the y-axis.

Alternatively, the optical sensing system 902 of the displacementmeasuring system 900 can be modified to allow for concurrently measuringthe displacement ΔX of the mass along the x-axis, e.g., corresponding tovibration in-and-out of page, and the displacement ΔY of the mass alongthe y-axis, e.g., corresponding to vibration left-and-right on page. Afirst modification of the optical sensing system 902 includesreplacement of the intensity pattern 910 with an intensity pattern thatencodes 2D spatial information, e.g., in the (x,y) plane, as describedbelow in connection with FIGS. 12A-12C. Another modification of theoptical sensing system 902 includes a modified configuration of theoptical source 906 that provides, as described below in connection withFIGS. 12A and 12D-12E, a pair of reference beams in addition to theprobe beam 908.

FIG. 12A is a plan view, e.g., in the (x,y) plane, of an intensitypattern 1210 that includes a plurality of hexagonal-shaped tiles 1212,each of which configured to redirect to the photodetector 920 lighthaving an intensity different from an intensity of light redirected tothe photodetector by any of its six adjacent tiles. In this example, theintensity pattern 1210 is a four-level intensity pattern that has tilesof first type 1212A, tiles of second type 1212B, tiles of third type1212A and tiles of fourth type 1212D arranged to form a unit cell 1214.Note that the honeycomb arrangement of the intensity pattern 1210 can begenerated by translating the unit cell 1214 in any of the eightdirections E, NE, N, NW, W, SW, S, SE.

FIG. 12B shows that a tile of first type 1212A is configured such that,when the probe beam 908 illuminates it, the redirected light 918 has anintensity I_(A) equal to maximum intensity I_(MAX), I_(A)=I_(MAX). Atile of fourth type 1212D is configured such that, when the probe beam908 illuminates it, the redirected light 918 has an intensity I_(D)equal to minimum intensity I_(MIN), I_(D)=I_(MIN). A tile of second type1212B is configured such that, when the probe beam 908 illuminates it,the redirected light 918 has a first intermediary intensity I_(B) thatsatisfies I_(MIN)<I_(B)<I_(MAX). And, a tile of third type 1212C isconfigured such that, when the probe beam 908 illuminates it, theredirected light 918 has a second intermediary intensity I_(C) thatsatisfies I_(MIN)<I_(C)<I_(B). The four types of tiles can redirectlight having any four arbitrary intensity levels. The above case is onlyan exemplary embodiment. As described above in connection with FIG. 9C,a photodiode of the photodetector 920 integrates, at a sampling time t,the redirected light 918 to provide a raw intensity value I(t) athreshold module. In the example shown in FIG. 12B, the threshold moduleof the photodetector 920 classifies the raw intensity value I(t) againstthreshold values Th_(AB), Th_(BC) and Th_(CD) in the following manner.If I(t)>Th_(AB), then the threshold module of the photodetector 920 canset I(t)=I_(A). If I(t)≤Th_(CD), then the threshold module of thephotodetector 920 can set I(t)=I_(D). If Th_(BC)≤I(t)<Th_(AB), then thethreshold module of the photodetector 920 can set I(t)=I_(B). IfTh_(CD)≤I(t)<Th_(BC), then the threshold module of the photodetector 920can set I(t)=I_(C). In some implementations, the threshold valuesTh_(AB), Th_(BC) and Th_(CD) can be predetermined. In otherimplementations, the threshold values Th_(AB), Th_(BC) and Th_(CD) canbe updated in an adaptive manner, as described below. In this manner,the photodetector 920 issues an intensity signal 1222 (shown in FIG.12F) that can have only four values {I_(D)=I_(MIN), I_(C), I_(B),I_(A)=I_(MAX)} and is related to the intensity of the light redirectedby the intensity pattern 1210 to the photodetector, as the intensitypattern carried by the mass 1164 is displaced along the x-axis and they-axis relative to the probe beam 908.

Referring again to FIG. 12A, the light source 906 provides, in additionto the probe beam 908 that forms the probe beam spot 916 as itilluminates a tile of the intensity pattern 1210, a first reference beamthat forms a first reference beam spot 1216A and a second reference beamthat forms a second reference beam spot 1216B. Note that a separationbetween each of the probe beam spot 916, the first reference beam spot1216A, and the second reference beam spot 1216B matches the separationbetween adjacent tiles of the intensity pattern 1210, such that thethree beams provided by the light source 906 always illuminate tiles ofdifferent types. In some implementations, the light source 906 includesan array of three VCSELs that emit the probe beam 908 and the pair ofthe reference beams. In other implementations, the light source 906includes an array of three LEDs that emit non-collimated light that arecoupled with one or more beam forming optics to provide the probe beam908 and the pair of the reference beams. FIG. 12C shows that redirectedlight associated with each of the first reference beam 1216A and thesecond reference beam 1216B can be sampled at slower rates relative tothe sampling rate of redirected light 918 associated with the probe beam908 to save power and bandwidth. Referring again to FIG. 12B, the lightsource 906's drive level and the photodetector 920's ADC level can beadjusted to correspond to an appropriate one of the levels I_(A), I_(B),I_(C), I_(D) of the intensity of the redirected light, based ondifferences between the detected intensity levels corresponding to theprobe beam 908 relative to the reference beams.

Moreover, in the example shown in FIG. 12A, the first reference beamspot 1216A and the second reference beam spot 1216B are cast on adjacenttiles located NE and E, respectively, relative to the tile on which theprobe beam spot 916 is cast. In this manner, once the processor 925determines a type of a tile on which the probe beam spot 916 iscurrently located, a combination of a level of intensity of lightredirected by the tile illuminated by the probe beam, a first level ofintensity of light redirected by a first adjacent tile illuminated bythe first reference beam, and a second level of intensity of lightredirected by a second adjacent tile illuminated by the second referencebeam can be only one from among combinations 1268 shown in FIG. 12B.

In accordance with combination 1268A, when the probe beam spot 916 iscast on a tile of first type 1212A, the first and second reference beamspots 1216A, 1216B are cast on adjacent tiles of second type 1212B andfourth type 1212D located NE and E, respectively, relative to the tileof first type 1212A. In accordance with combination 1268B, when theprobe beam spot 916 is cast on a tile of second type 1212B, the firstand second reference beam spots 1216A, 1216B are cast on adjacent tilesof first type 1212A and third type 1212C located NE and E, respectively,relative to the tile of second type 1212B. In accordance withcombination 1268C, when the probe beam spot 916 is cast on a tile ofthird type 1212C, the first and second reference beam spots 1216A, 1216Bare cast on adjacent tiles of fourth type 1212D and second type 1212Blocated NE and E, respectively, relative to the tile of third type1212C. In accordance with combination 1268D, when the probe beam spot916 is cast on a tile of fourth type 1212D, the first and secondreference beam spots 1216A, 1216B are cast on adjacent tiles of thirdtype 1212C and first type 1212A located NE and E, respectively, relativeto the tile of fourth type 1212D.

The combinations 1268A, 1268B, 1268C and 1268D of three signal levelsissued by the photodetector 920 can be used to adaptively update thethreshold values Th_(AB), Th_(BC), Th_(CD) in the following manner. Forinstance, the photodetector 920 can issue, for a sampling time t and thefirst combination 1268A, a first set of raw intensity values {I₁₁₆(t),I_(416A)(t), I_(416B)(t)} corresponding to the redirected probe beam908, the first reference beam, and the second reference beam,respectively, that will be classified as a first set of intensity values{I_(A), I_(B), I_(D)}; for a sampling time t′ and the second combination1268B, a second set of raw intensity values {I₁₆₆(t′), I_(416A)(t′),I_(416B)(t′)} corresponding to the redirected probe beam 908, the firstreference beam, and the second reference beam, respectively, that willbe classified as a second set of intensity values {I_(B), I_(A), I_(C)};for a sampling time t″ and the third combination 1268C, a third set ofraw intensity values {I₁₁₆(t″), I_(416A)(t″), I_(416B)(t″)}corresponding to the redirected probe beam 908, the first referencebeam, and the second reference beam, respectively, that will beclassified as a third set of intensity values {I_(C), I_(D), I_(B)}; fora sampling time t″ and the fourth combination 1268D, a fourth set of rawintensity values {I₁₁₆(t′″), I_(416A)(t′″), I_(416B)(t′″)} correspondingto the redirected probe beam 908, the first reference beam, and thesecond reference beam, respectively, that will be classified as a fourthset of intensity values {I_(D), I_(C), I_(A)}; and so on and so forth.

Moreover, the photodetector can include a digital low pass filter (LPF)1270 configured to obtain a first statistic<I>_(A) of the raw intensityvalues that have been associated with the intensity value I_(A), where<I>_(A)=<{I₁₁₆(t), I_(416A)(t′), I_(416B)(t′″), . . . }>; a secondstatistic<I>_(B) of the raw intensity values that have been associatedwith the intensity value I_(B), where <I>_(B)=<{I_(416A)(t), I₁₁₆(t′),I_(416B)(t″), . . . }>; a third statistic<I>_(C) of the raw intensityvalues that have been associated with the intensity value I_(C), where<I>_(C)=<{I_(416B)(t′), I₁₁₆(t″), I_(416A)(t′″), . . . }>; and a fourthstatistic<I>_(D) of the raw intensity values that have been associatedwith the intensity value I_(D), where <I>_(D)=<{I_(416B)(t),I_(416A)(t″), I₁₁₆(t′″), . . . }>. Here, the statistic denoted<I>_(X)can be a median, mean, truncated mean, maximum or minimum of a set ofraw intensity values classified as the intensity level I_(X), where thesubscript X is {A, B, C or D}. In this manner, the digital LPF canadaptively update the threshold Th_(AB) used by the threshold module toset the intensity values I_(A) or I_(B) asTh_(AB)=(1/2)(<I>_(A)−<I>_(B)); the threshold Th_(BC) used by thethreshold module to set the intensity values I_(B) or I_(C) asTh_(BC)=(1/2)(<I>_(B)−<I>_(C)); and the threshold Th_(CD) used by thethreshold module to set the intensity values I_(C) or I_(D) asTh_(CD)=(1/2)(<I>_(C)−<I>_(D)). The foregoing operations performed bythe digital LPF of the photodetector 920 amount to a procedure forself-calibrating (also referred to as a procedure for backgroundcalibrating) the optical sensing system 902 that uses the intensitypattern 1210.

FIG. 12D shows that the four types of tiles of the intensity pattern1210 form six possible tile borders 1213 across which the intensity ofthe redirected light 918 changes by a fraction of the intensity rangeI_(MAX)−I_(MIN). In the first row of FIG. 12D, the intensity ofredirected light 918 changes by (1/3)(I_(MAX)−I_(MIN)) for each of atile border 1213AB formed between a tile of first type 1212A and a tileof second type 1212B, a tile border 1213BC formed between a tile ofsecond type 1212B and a tile of third type 1212C, and a tile border1213CD formed between a tile of third type 1212C and a tile of fourthtype 1212D. In the second row of FIG. 12D, the intensity of redirectedlight 918 changes by (2/3)(I_(MAX)−I_(MIN)) for each of a tile border1213AC formed between a tile of first type 1212A and a tile of thirdtype 1212C, and a tile border 1213BD formed between a tile of secondtype 1212B and a tile of fourth type 1212D. And, in the third row ofFIG. 12D, the intensity of redirected light 918 changes by(I_(MAX)−I_(MIN)) for a tile border 1213AD formed between a tile offirst type 1212A and a tile of fourth type 1212D.

Referring again to FIG. 12A, note that the tile borders of the intensitypattern 1210 are distributed at known locations relative to each otherin the (x,y) plane, so this intensity pattern can be used, as part ofthe optical sensing system 902 of the displacement measuring system 900,by the processor 925 to concurrently measure the mass 1164'sdisplacement ΔX along the x-axis and displacement ΔY along the y-axis.Note that during the motion of the mass 1164, the intensity pattern 1210moves (along with the mass) relative to a probe beam spot 916corresponding to the probe beam 908 that illuminates the intensitypattern, one tile at a time. In this manner, multiple tile bordercrossings will occur as the intensity pattern 1210 is displaced in the(x,y) plane, where for each tile border crossing, a tile border formedbetween adjacent tiles of different type crosses through the beam spot916 associated with the static probe beam 908.

FIG. 12E shows that for each type of tile, there are 6 possible tileborder crossings, three out of which are ambiguously paired. When theprobe beam 908 illuminates a tile of first type 1212A, first tile bordercrossings 1228A will occur when (i) the tile border 1213AB crosses theprobe beam, so the probe beam then illuminates either the tile of secondtype 1212B that is disposed on the NE side of the tile of first type1212A or the tile of second type 1212B that is disposed on the SW of thetile of first type 1212A; (ii) the tile border 1213AD crosses the probebeam, so the probe beam then illuminates either the tile of fourth type1212D that is disposed on the E side of the tile of first type 1212A orthe tile of fourth type 1212D that is disposed on the W of the tile offirst type 1212A; and (iii) the tile border 1213AC crosses the probebeam, so the probe beam then illuminates either the tile of third type1212C that is disposed on the SE side of the tile of first type 1212A orthe tile of third type 1212C that is disposed on the NW of the tile offirst type 1212A.

Further, when the probe beam 908 illuminates a tile of fourth type1212D, fourth tile border crossings 1228D will occur when (i) the tileborder 1213CD crosses the probe beam, so the probe beam then illuminateseither the tile of third type 1212C that is disposed on the NE side ofthe tile of fourth type 1212D or the tile of third type 1212C that isdisposed on the SW of the tile of fourth type 1212D; (ii) the tileborder 1213AD crosses the probe beam, so the probe beam then illuminateseither the tile of first type 1212A that is disposed on the E side ofthe tile of fourth type 1212D or the tile of first type 1212A that isdisposed on the W of the tile of fourth type 1212D; and (iii) the tileborder 1213BD crosses the probe beam, so the probe beam then illuminateseither the tile of second type 1212B that is disposed on the SE side ofthe tile of fourth type 1212D or the tile of second type 1212B that isdisposed on the NW of the tile of fourth type 1212D.

Furthermore, when the probe beam 908 illuminates a tile of second type1212B, second tile border crossings 1228B will occur when (i) the tileborder 1213AB crosses the probe beam, so the probe beam then illuminateseither the tile of first type 1212A that is disposed on the NE side ofthe tile of second type 1212B or the tile of first type 1212A that isdisposed on the SW of the tile of second type 1212B; (ii) the tileborder 1213BC crosses the probe beam, so the probe beam then illuminateseither the tile of third type 1212C that is disposed on the E side ofthe tile of second type 1212B or the tile of third type 1212C that isdisposed on the W of the tile of second type 1212B; and (iii) the tileborder 1213BD crosses the probe beam, so the probe beam then illuminateseither the tile of fourth type 1212D that is disposed on the SE side ofthe tile of second type 1212B or the tile of fourth type 1212D that isdisposed on the NW of the tile of second type 1212B.

Also, when the probe beam 908 illuminates a tile of third type 1212C,third tile border crossings 1228C will occur when (i) the tile border1213CD crosses the probe beam, so the probe beam then illuminates eitherthe tile of fourth type 1212D that is disposed on the NE side of thetile of third type 1212C or the tile of fourth type 1212D that isdisposed on the SW of the tile of third type 1212C; (ii) the tile border1213BC crosses the probe beam, so the probe beam then illuminates eitherthe tile of second type 1212D that is disposed on the E side of the tileof third type 1212C or the tile of second type 1212B that is disposed onthe W of the tile of third type 1212C; and (iii) the tile border 1213ACcrosses the probe beam, so the probe beam then illuminates either thetile of first type 1212A that is disposed on the SE side of the tile ofthird type 1212C or the tile of first type 1212A that is disposed on theNW of the tile of third type 1212C.

Referring again to FIG. 12A, a probe beam spot 916 corresponding to theprobe beam 908 illuminates (i) a tile of first type 1212A at a departurepoint (labeled “START”) when the motion of the mass 1164 begins, and(ii) a tile of fourth type 1212D at an arrival point (labeled “END”)when the motion of the mass ends. During this motion of the mass, therehave been successive tile border crossings at unknown points P_(C1),P_(C2), P_(C3). The times when these tile border crossings occur andtheir exact location in the (x,y) plane is determined by the processor925 in the following manner.

An intensity signal 1222 issued by the photodetector 920 relates to theintensity of the light redirected by the intensity pattern 1210 to thephotodetector. FIG. 12F shows changes in the intensity signal 1222caused by the multiple tile border crossings that occur as the intensitypattern 1210 carried by the mass 1164 is displaced relative to the probebeam spot 916 from the departure point to the arrival point. Asdescribed above in connection with FIG. 9C, the tile border crossingsoccur at times t₁, t₂, t₃ corresponding to predefined changes of theintensity signal 1222, e.g., corresponding ones the predefined changesshown in FIG. 12D: ±(1/3)ΔI, ±(2/3)ΔI, or ±ΔI, whereΔI=(I_(MAX)−I_(MIN)).

Additionally, a first displacement signal ΔX_(bEMF)(t) 1240X associatedwith the displacement ΔX of the mass 1164 along the x-axis is acquiredby the bEMF sensing system 930 concurrently with the intensity signal1222. FIG. 12G shows the first displacement signal ΔX_(bEMF)(t) 1240Xacquired, from a start time is to an end time t_(E), while the mass 1164is displaced relative to the probe beam spot 916 from the departurepoint to the arrival point. As a slope of the first displacement signalΔX_(bEMF)(t) 1240X is negative (due to a non-zero westward component ofthe mass 1164's velocity) over the entire time interval (t_(E)−t_(S)),the processor 925 determines that the direction of motion of the mass1164 has a non-zero westward component over the entire time interval(t_(E)−t_(S)).

Referring again to FIG. 12F, the processor 925 determines that the firsttile border crossing that occurs at t₁ causes a decrease of2/3(I_(MAX)−I_(MIN)) of the intensity signal 1222. As such, theprocessor 925 determines, based on the second row of FIG. 12D, that thefirst tile border crossing that occurs at t₁ is across either (i) a tileborder 1213AC, in which case the probe beam spot 916 transitions onto atile of third type 1212C; or (ii) a tile border 1213BD, in which casethe probe beam spot 916 transitions onto a tile of fourth type 1212D. Inthe first case (i), the first reference spot 1216A transitions onto atile of fourth type 1212D and the second reference spot 1216Btransitions onto a tile of second type 1212B. In the second case (ii),the first reference spot 1216A transitions onto a tile of third type1212C and the second reference spot 1216B transitions onto a tile offirst type 1212A. In the example illustrated in FIG. 12A, the differencebetween intensity of redirected light associated with the probe beamspot 916 and intensity of redirected light associated with the firstreference spot 1216A is −(1/3)(I_(MAX)−I_(MIN)); and the differencebetween intensity of redirected light associated with the probe beamspot 916 and intensity of redirected light associated with the secondreference spot 1216B is +(1/3)(I_(MAX)−I_(MIN)). This corresponds tocase (i), and contradicts case (ii). In this manner, the processor 925determines that, from the start time t_(S) to the time t₁ when the firsttile border crossing occurs across a tile border 1213AC, the probe beamspot 916 is cast on a tile of first type 1212A; and, from the time t₁ tothe time t₂ when a second tile border crossing occurs, the probe beamspot 916 is cast on a tile of third type 1212C. Then, the processor 925determines, based on FIG. 12E, that the probe beam spot 916 is cast oneither the tile of third type 1212C that is disposed on the SE side ofthe tile of first type 1212A or the tile of third type 1212C that isdisposed on the NW side of the tile of first type 1212A. Here, theprocessor 925 uses the previous determination, made based on the firstdisplacement signal ΔX_(bEMF)(t) 1240X, that the direction of motion ofthe mass 1164 has a non-zero westward component over the entire timeinterval (t_(E)−t_(S)).

In this manner, the processor 925 determines that, from the start timet_(S) to the time t₁ (when the first tile border crossing occurs acrossa tile border 1213AC), the probe beam spot 916 is cast on a tile offirst type 1212A; and, from the time t₁ to the time t₂ (when a secondtile border crossing occurs), the probe beam spot 916 is cast on a tileof third type 1212C that is disposed on the NW side of the tile of firsttype 1212A. As such, by time t₁ when the first tile border crossingoccurs, the mass 1164 has moved about one size of a tile westward andabout one half of the size of the tile northward from the startingpoint.

Further, the processor 925 determines that the second tile bordercrossing that occurs at t₂ causes an increase of 1/3(I_(MAX)−I_(MIN)) ofthe intensity signal 1222. As such, the processor 925 determines, basedon the first row of FIG. 12D, that the second tile border crossing thatoccurs at t₂ is across a tile border 1213BC, in which case the probebeam spot 916 transitions from the current tile of third type 1212C ontoa tile of second type 1212B. Then, the processor 925 determines, basedon FIG. 12E, that the probe beam spot 916 is cast on either the tile ofsecond type 1212B that is disposed on the E side of the tile of thirdtype 1212C or the tile of second type 1212B that is disposed on the Wside of the tile of third type 1212C. Here, the processor 925 uses theprevious determination, made based on the first displacement signalΔX_(bEMF)(t) 1240X, that the direction of motion of the mass 1164 has anon-zero westward component over the entire time interval (t_(E)−t_(S)).

In this manner, the processor 925 determines that, from the time t₁(when the first tile border crossing occurs across a tile border 1213AC)to the time t₂ (when the second tile border crossing occurs across atile border 1213BC), the probe beam spot 916 is cast on a tile of thirdtype 1212C; and, from the time t₂ to the time t₃ (when a third tileborder crossing occurs), the probe beam spot 916 is cast on a tile ofsecond type 1212B that is disposed on the W side of the tile of thirdtype 1212C. As such, by time t₂ when the second tile border crossingoccurs, the mass 1164 has moved about two sizes of the tile westward andabout one size of the tile northward from the starting point.

Furthermore, the processor 925 determines that the third tile bordercrossing that occurs at t₃ causes a decrease of 2/3(I_(MAX)−I_(MIN)) ofthe intensity signal 1222. As such, the processor 925 determines, basedon the second row of FIG. 12D, that the third tile border crossing thatoccurs at t₃ is across a tile border 1213BD, in which case the probebeam spot 916 transitions from the current tile of second type 1212Bonto a tile of fourth type 1212D. Then, the processor 925 determines,based on FIG. 12E, that the probe beam spot 916 is cast on either thetile of fourth type 1212D that is disposed on the SE side of the tile ofsecond type 1212B or the tile of fourth type 1212D that is disposed onthe NW side of the tile of second type 1212B. Here, the processor 925uses the previous determination, made based on the first displacementsignal ΔX_(bEMF)(t) 1240X, that the direction of motion of the mass 1164has a non-zero westward component over the entire time interval(t_(E)−t_(S)).

In this manner, the processor 925 determines that, from the time t₂(when the second tile border crossing occurs across a tile border1213BC) to the time t₃ (when the third tile border crossing occursacross a tile border 1213BD), the probe beam spot 916 is cast on a tileof second type 1212B; and, from the time t₃ to the end time t_(E), theprobe beam spot 916 is cast on a tile of fourth type 1212D that isdisposed on the NW side of the tile of second type 1212B. As such, bytime t₃ when the third tile border crossing occurs, the mass 1164 hasmoved about three sizes of the tile westward and more than one and ahalf size of the tile northward from the starting point.

The processor 925 uses the foregoing information determined based on (i)the changes of the intensity signal 1222 and (ii) the slope of the firstdisplacement signal ΔX_(bEMF)(t) 1240X to determine a seconddisplacement signal ΔX_(OPT)(t) 1242X associated with the displacementΔX of the mass 1164 along the x-axis, and a second displacement signalΔY_(OPT)(t) 1242Y associated with the displacement ΔY of the mass 1164along the y-axis. FIG. 12H shows the second displacement signalΔY_(OPT)(t) 1242Y associated with the displacement ΔY of the mass 1164along the y-axis corresponding to the trip in the (x,y) plane from thestarting point to the ending point, as shown in FIG. 12A. Note that, asthe second displacement signal ΔY_(OPT)(t) 1242Y includes only they-coordinates of the crossing points P_(C1), P_(C2), P_(C3), aresolution of the second displacement signal ΔY_(OPT)(t) 1242Y is about10 μm to 50 μm corresponding to a feature size of the intensity pattern1210.

FIG. 12I shows (represented by filled diamonds) the second displacementsignal ΔX_(OPT)(t) 1242X associated with the displacement ΔX of the mass1164 along the x-axis corresponding to the trip in the (x,y) plane fromthe starting point to the ending point, as shown in FIG. 12A. Note that,as the second displacement signal ΔX_(OPT)(t) 1242X includes only thex-coordinates of the crossing points P_(C1), P_(C2), P_(C3), aresolution of the second displacement signal ΔX_(OPT)(t) 1242X is about10 μm to 50 μm, corresponding to a feature size of the intensity pattern1210.

FIG. 12I also shows a displacement signal ΔX(t) 1244X associated withthe displacement ΔX of the mass 1164 along the x-axis corresponding tothe trip in the (x,y) plane from the starting point to the ending point,as shown in FIG. 12A. Here, the processor 925 determines thedisplacement signal ΔX(t) 1244X by interpolating the previouslydetermined second displacement signal ΔX_(OPT)(t) 1242X with the firstdisplacement signal ΔX_(bEMF)(t) 1240X, by using the interpolationtechnique described above in connection with FIG. 10A. Note that,because the displacement signal ΔX(t) 1244X includes, in addition to thex-coordinates of the crossing points P_(C1), P_(C2), P_(C3), thex-components of the points between the starting point and the endingpoint of the trip as determined by the bEMF sensing system 930, aresolution of the displacement signal ΔX(t) 1244X is about 1 μm,corresponding to the resolution of the bEMF sensing system.

Referring again to FIG. 9A, several optical structures can be used toredirect the probe beam 908 that illuminates the intensity pattern 910to the photodetector 920. In some implementations, these opticalstructures are configured to use a reflective intensity pattern 910. Inother implementations, these optical structures are configured to use atransmissive intensity pattern 910 in conjunction with one or morereflective elements.

FIG. 13A shows an example of an optical structure 1310A that includes asubstrate 1374 having a first surface 1376 and a second surface 1378opposing the first surface. The first surface 1376 is to be coupled witha surface 1165 of the mass 1164 that is spaced apart from and facing thelight source 906 and the photodetector 920. The second surface 1378 isconfigured with a structure that includes facets that are tiltedrelative to the probe beam 908. Here, a reflective intensity pattern 910is attached to the second surface 1378, such that the probe beam 908illuminates the reflective intensity pattern, one-tile-at-a-time. A tiltof the facets of the second surface 1378 is configured such that thereflective intensity pattern 910 redirects the probe beam 908 as aredirected beam 918 to the photodetector 920, regardless of adisplacement ΔX along the x-axis of the reflective intensity patternrelative to the probe beam. In this example, different tiles of thereflective intensity pattern 910 have different reflectivities, suchthat light redirected to the photodetector 920 from adjacent tiles hasdifferent intensities.

FIG. 13B shows another example of an optical structure 1310B thatincludes a micro-mirror array 1380 to be mounted on a surface 1165 ofthe mass 1164 that is spaced apart from and facing the light source 906and the photodetector 920. A transmissive intensity pattern 910 iscoupled with the micro-mirror array 1380, such that the latter issandwiched between the surface 1165 of the mass 1164 and thetransmissive intensity pattern 910. As such, the probe beam 908illuminates the transmissive intensity pattern 910, one-tile-at-a-time.In this manner, the probe beam 908 is selectively transmitted throughthe transmissive intensity pattern 910 to reflectors 1382 of themicro-mirror array 1380. The reflectors 1382 of the micro-mirror array1380 are tilted relative to the transmitted probe beam 908 to reflect itas a redirected beam 918 to the photodetector 920, regardless of adisplacement ΔX along the x-axis of the transmissive intensity pattern910 relative to the probe beam. In this example, different tiles of thetransmissive intensity pattern 910 have different transmissivities, suchthat light redirected to the photodetector 920 from adjacent tiles hasdifferent intensities.

FIG. 13C shows another example of an optical structure 1310C thatincludes a substrate 1375 having a first surface 1376 and a secondsurface 1380 opposing the first surface. The substrate 1375 includesglass, plastic, or other material that is transparent to light providedby the light source 906. The first surface 1376 is to be coupled with asurface 1165 of the mass 1164 that is spaced apart from and facing thelight source 906 and the photodetector 920. The optical structure 1310Cfurther includes a scattering layer 1382 sandwiched between the firstsurface 1376 and the surface 1165 of the mass 1164. A transmissiveintensity pattern 910 is disposed on the second surface 1380, such thatthe probe beam 908 illuminates the transmissive intensity pattern,one-tile-at-a-time. In this manner, the probe beam 908 is selectivelytransmitted through the transmissive intensity pattern 910 and throughthe substrate 1375 to the scattering layer 1382. A scattering structureof the scattering layer 1382 is configured such that the scatteringlayer scatters the transmitted probe beam 908 as a redirected beam 918to the photodetector 920, regardless of a displacement ΔX along thex-axis of the transmissive intensity pattern 910 relative to the probebeam.

FIG. 14A shows another example of an optical structure 1410A thatincludes a substrate 1375 having a first surface 1484 and a secondsurface 1380 opposing the first surface. The substrate 1375 includesglass, plastic, or other material that is transparent to light providedby the light source 906. The optical structure 1410A further includes adiffusive layer 1382 disposed on the first surface 1484 to render thefirst surface diffusely reflective. A transmissive intensity pattern 910is disposed on the second surface 1380, such that the probe beam 908illuminates the transmissive intensity pattern, one-tile-at-a-time. Inthis manner, the probe beam 908 is selectively transmitted through thetransmissive intensity pattern 910 and through the substrate 1375 to thediffusely reflective first surface 1484. The first surface 1484 isfurther configured with a structure that includes facets that are tiltedrelative to the transmitted probe beam 908. A tilt of the facets of thefirst surface 1484 is configured such that the first surface diffuselyreflects the probe beam 908 as a redirected beam 918 to thephotodetector 920, regardless of a displacement ΔX along the x-axis ofthe reflective intensity pattern relative to the probe beam.

FIG. 14B shows another example of an optical structure 1410B thatincludes a substrate 1375 having a first surface 1486 and a secondsurface 1380 opposing the first surface. The substrate 1375 includesglass, plastic, or other material that is transparent to light providedby the light source 906. A transmissive intensity pattern 910 isdisposed on the second surface 1380, such that the probe beam 908illuminates the transmissive intensity pattern, one-tile-at-a-time. Inthis manner, the probe beam 908 is selectively transmitted through thetransmissive intensity pattern 910 and through the substrate 1375 to thefirst surface 1486. The first surface 1486 is further configured with astructure that includes facets that are tilted relative to thetransmitted probe beam 908. A tilt of the facets of the first surface1486 is configured such that the first surface reflects via totalinternal reflection (TIR) the probe beam 908 as a redirected beam 918 tothe photodetector 920, regardless of a displacement ΔX along the x-axisof the reflective intensity pattern relative to the probe beam.

FIG. 14C shows a technique for mounting the optical structure 1410A or1410B to the moving mass 1164. Mounting tabs 1488 can be set proud ofthe light redirecting structure to provide a gap 1490 from the movingmass 1164 of effective height Z_(GAP). The mounting tabs 1488 also set adatum to allow precision tolerance fitting, e.g., to determine athickness of adhesive 1492 used to attach the optical structure 1410A or1410B to the moving mass 1164. When mounting the optical structure1410A, the gap 1490 can be an air gap or can be filed with a fillermaterial. When mounting the optical structure 1410B, the gap 1490 is anair gap. In this case, this air gap is important for maximizing thecontrast of refractive index at the first surface 1486 to optimizeoptical performance.

In some implementations, a VCSEL, whether singular or in array form, canhave an efficiency of 300 lm/W. In some implementations, the VCSEL(s) ofthe light source 906 can be operated using peak currents in the range of1-10 mA, and peak voltages in the range of 1-2V, for a maximum powerconsumption of 1-10 mW. As this power would be consumed if the VCSEL(s)were run continuously, the actual power used the VCSEL(s) can 100-1000times smaller, as typical VCSEL(s) operation is duty cycled.

As noted above in connection with FIG. 9C and FIG. 12B, thephotodetector 920 senses the change in light intensity and uses it todetect tile border crossings between tiles of the intensity pattern,e.g., 910 and 1210, as a result of their relative lateral motion ΔX andaxial motion ΔY. In some implementations, threshold hysteresis can beused to reliably detect level transition. In such cases, in order toavoid false tile border crossings, a tile border crossing is determinedwhile moving in a forward direction, then the same tile border crossingis determined again while moving in a backward direction.

In some implementations, processing electronics 925 can be configured asmixed signal circuitry that processes analog signals and digitalsignals. In some implementations, processing electronics 925 can beconfigured as one or more digital signal processors, e.g., ASIC, FPGA,CPU, etc.

FIG. 15A is a side view, e.g. in the (x,z) plane, of an example of adisplacement measuring system 1500A configured to measure displacementof a mass 1534. Here, a haptic engine 1530A having a frame 1532Aencapsulates the mass 1534 and at least a portion of the displacementmeasuring system 1500A. In this example, the displacement measuringsystem 1500A includes a mount 1502A that has a surface 1503XY and isattached on an opposing surface to a surface of the frame 1532A that isparallel to the (x,y) plane. The displacement measuring system 1500Afurther includes a light emitting element (LEE) array 1504 disposed onthe surface 1503XY of the mount 1502A, an intensity pattern 1510Acoupled with a surface 1535XY of the mass 1534, and a photodetector 1522disposed on the same surface 1503XY of the mount as the LEE array 1504.A surface 1511 of the intensity pattern 1510A is spaced apart from andfaces both the LEE array 1504 and the photodetector 1522. In thismanner, during operation of the displacement measuring system 1500A, theLEE array 1504 illuminates the surface 1511 of the intensity pattern1510A with N_(TOT) beams 1506, and the intensity pattern redirects, tothe photodetector 1522, at least some of the light impinging on theilluminated surface, such that N_(TOT) redirected beams 1520A form anacute angle relative the illuminating beams.

FIG. 15B is a side view, e.g. in the (x,z) plane, of another example ofa displacement measuring system 1500B configured to measure displacementof the mass 1534. Here, another haptic engine 1530B having a frame 1532Bencapsulates the mass 1534 and at least a portion of the displacementmeasuring system 1500B. In this example, the displacement measuringsystem 1500B includes a mount 1502B that has a surface 1503XY and anangled surface 1503YZ. In some cases, the angled surface 1530XZ can beoriented to form a substantially right angle relative to the surface1503XY. A surface of the mount 1502B opposing the surface 1503XY isattached to a surface of the frame 1532B that is parallel to the (x,y)plane, and another surface of the mount opposing the surface 1503YZ isattached to another surface of the frame 1532B that can be parallel tothe (y,z) plane. The displacement measuring system 1500B furtherincludes the LEE array 1504 disposed on the surface 1503XY of the mount1502B, an intensity pattern 1510B coupled with a surface 1535XY of themass 1534, and the photodetector 1522 disposed on the surface 1503YZ ofthe mount. The intensity pattern 1510B has the surface 1511 that isspaced apart from and faces the LEE array 1504, and a surface 1516 thatis spaced apart from and faces the photodetector 1522. In this manner,during operation of the displacement measuring system 1500B, the LEEarray 1504 illuminates the surface 1511 of the intensity pattern 1510Bwith the N_(TOT) beams 1506, and the intensity pattern redirects,through the surface 1516 to the photodetector 1522, at least some of thelight impinging on the illuminated surface, such that N_(TOT) redirectedbeams 1520B form a folding angle relative to the beams 1506. In somecases, the folding angle is a substantially right angle.

FIG. 15C is a plan view, e.g., in the (x,y) plane, of the surface 1511of the intensity pattern 1510A/1510B. The intensity pattern 1510A/1510Bincludes a plurality of tiles 1512 separated from each other bycorresponding tile borders 1513. Each tile 1512 of the intensity pattern1510A/1510B is configured to redirect to the photodetector 1522 lighthaving an intensity different from an intensity of light redirected tothe photodetector by any of its adjacent tiles. In the example shown inFIG. 15C, the intensity pattern 1510A/1510B is a binary intensitypattern because each tile 1512A (or 1512B) has only two adjacent tiles1512B (or 1512A) configured to redirect to the photodetector 1522 lighthaving the same intensity. As such, the binary intensity pattern1510A/1510B has M=2 tile types: tiles of first type 1512A and tiles ofsecond type 1512B, where each tile of first type 1512A forms respectivetile borders 1513 with two adjacent tiles of second type 1512B, and eachtile of second type 1512B forms respective tile borders 1513 with twoadjacent tiles of first type 1512A. A tile of first type 1512A isconfigured such that, when one of the beams 1506 illuminates it, thecorresponding one of the redirected beams 1520A/1520B has a maximumintensity I_(MAX). Further, a tile of second type 1512B is configuredsuch that, when one of the beams 1506 illuminates it, the correspondingone of the redirected beams 1520A/1520B has a minimum intensity I_(MIN),where I_(MIN)<I_(MAX). Here, the tile borders 1513 are distributed atknown locations relative to each other along the x-axis, so the binaryintensity pattern 1510A/1510B can be used as part of the displacementmeasuring system 1500A/1500B to measure displacement ΔX of the mass 1534along the x-axis. An example of a four-level intensity pattern 1810 of adisplacement measuring system 1800, that has M=4 tile types, can be usedto measure, as described below in connection with FIGS. 18A-18E,displacement ΔX of the mass 1534 along the x-axis and displacement ΔY ofthe mass along the y-axis.

Referring again to FIG. 15C, in some implementations, the intensitypattern 1510A can be configured to have a reflective surface 1511 thatselectively reflects, scatters or both the illuminating beams 1506 tothe photodetector 1522 as redirected beams 1520A. In such cases, a tileof first type 1512A (shown in white) has a first reflectivity R₁, and atile of second type 1512B (shown in grey) has a second reflectivity R₂,smaller than the first reflectivity. For example, the secondreflectivity R₂ can be at most half the first reflectivity R₁, e.g.,R₂=0.3R₁, 0.1R₁, 0.05R₁ or other fractions of R₁. For example, the tileof first type 1512A can be coated with a reflective film and the tile ofsecond type 1512B can be coated with an absorptive film. As anotherexample, the tile of first type 1512A can be coated with a multilayerreflection coating and the tile of second type 1512B can be coated witha multilayer anti-reflection coating.

In some implementations, the intensity pattern 1510B can be configuredas a combination of a transmissive surface 1511, an array ofmicro-mirrors 1518 (or micro-prisms, or other redirectingmicro-structures), and a transmissive surface 1516. In this manner, thetransmissive surface 1511 selectively transmits the illuminating beams1506, the array of micro-mirrors 1518 reflects, scatters or both theselectively transmitted beams, and the transmissive surface 1516transmits the redirected beams 1520B to the photodetector 1522. In suchcases, a tile of first type 1512A (shown in white) has a firsttransmissivity T₁, and a tile of second type 1512B (shown in grey) has asecond transmissivity T₂, smaller than the first transmissivity. Forexample, the second transmissivity T₂ can be at most half the firsttransmissivity T₁, e.g., T₂=0.3T₁, 0.1T₁, 0.05T₁ or other fractions ofT₁.

FIG. 15C also shows that the N_(TOT) beams 1506 illuminate an area 1514of the surface 1511 of the intensity pattern 1510A/1510B with discretebeam spots 1508 separated by a known separation δ. The separation δbetween adjacent beam spots determines the spatial resolution of thedisplacement measurements performed by the displacement measuring system1500A/1500B. For the examples of displacement measurement systemsdescribed in this specification, the separation δ between adjacent beamspots can be as small as about 1 μm, and as large as a size along thex-axis of each tile 1512. In addition, a combination of the separation δbetween adjacent beam spots and a size along the x-axis of each tile1512 determines a number N of beams from among the N_(TOT) beams 1506provided by the LEE array 1504 that can concurrently illuminate thetile. In order for the displacement measuring system 1500A/1500B toresolve both direction and magnitude of the displacement ΔX of the mass1534 along the x-axis, the number N of the N_(TOT) beams 1506 can bepredetermined, based on the number M of tile types, in the followingmanner. In some implementations, if an intensity pattern has M≥2 tiletypes, then a number N from among the N_(TOT) beams 1506 that canconcurrently illuminate each tile satisfies the conditions 2≤N≤N_(TOT).In the examples shown in FIGS. 15A-15C, the LEE array 1504 providesN_(TOT)=4 beams 1506, and the size of each tile 1512 of the intensitypattern 1510A/1510B allows for N=2 from among the 4 beams 1506 toilluminate each tile. In other implementations, if an intensity patternhas M≥3 tile types, then a number N from among the N_(TOT) beams 1506that can concurrently illuminate each tile satisfies the conditions1≤N≤N_(TOT), e.g., as described below in connection with FIG. 17A.

Referring again to FIGS. 15A-15B, the displacement measuring system1500A/1500B includes a controller system 1525 that is linked to the LEEarray 1504 and the photodetector 1522, and is configured to control theway the photodetector captures individual ones the N_(TOT) redirectedbeams 1520A/1520B associated with corresponding ones of the N_(TOT)illuminating beams 1506. FIG. 15D shows that the controller system 1525includes a pulse-width modulation (PWM) driver 1536 and a processor1546, and that, in this example, the LEE array 1504 includes N_(TOT)≥2light emitting elements (LEEs) 1528 that are independently switchable.In this manner, the LEEs 1528 of the LEE array 1504 can be PWM-switchedat maximum current, so no adjustable current level is needed for the LEEarray 1504. Further, the photodetector 1522 includes a singlephoto-diode 1538, an integration capacitance 1540, a switch 1542, and ananalog-to-digital converter (ADC) 1544.

In some implementations, each LEE 1528 of the LEE array 1504 includes arespective VCSEL that emits, when switched ON by the PWM driver 1536,one of the N_(TOT) beams 1506 that illuminate the intensity pattern1510A/1510B. In some implementations, each LEE 1528 of the LEE array1504 includes a respective LED and a beam-shaping optic (not shown inFIGS. 15A-15B, 15D) that is optically coupled with the LED. In thiscase, the respective LED emits, when switched ON by the PWM driver 1536,un-collimated light, and the beam-shaping optic receives theun-collimated light and issues one of the N_(TOT) beams 1506 thatilluminate the intensity pattern 1510A/1510B. In this manner, in eitherof these implementations, the beam spot 1508 over which the intensitypattern 1510A/1510B is illuminated by each of the beams 1506 has a sizeof 20 μm, 10 μm, or smaller.

Moreover, the processor 1546 can instruct the PWM driver 1536 toindividually switch ON/OFF the LEEs 1528 of the LEE array 1504, suchthat the beams 1506 successively illuminate the intensity pattern1510A/1510B, on a one-beam-at-a-time basis. To do so, the PWM driver1536 can use a switching gate 1524 like the one shown in FIG. 15E. Here,the switching gate 1524 is a sequence of trains of pulses, each trainincluding N_(TOT) pulses corresponding to the N_(TOT) LEEs 1528 of theLEE array 1504. Each pulse has a pulse duration T_(A) during which asingle corresponding LEE 1528 is ON while the other (N_(TOT)−1) LEEs ofthe LEE array 1504 are OFF and the switch 1542 is open. The pulses areseparated from each other by a reset duration T_(R), during which theswitch 1542 is closed. Note that operation of the photodetector 1522 incharge integration mode, using the switching gate 1524 as describedbelow, can beneficially provide exposure time control. Additionally, thetrains are repeated in time with a period T_(S) that represents asampling period, related to the sampling rate f_(S)=1/T_(S). As such, atrain of pulses can correspond to a sampling time t₀, the next train ofpulses corresponds to the next sampling time t₁, the next train ofpulses corresponds to the next sampling time t₂, and so on. Moreover,the pulse duration T_(A) and the reset time T_(R) can be 10, 100, or1000 time smaller than the sampling period T_(S). Note that theprocessor 1546 can adjust either the duty cycle of the LEE array 1504 orthe integration capacitance 1540 of the photodetector 1522 or both to(i) control the dynamic range of the displacement measuring system1500A/1500B; and (ii) ensure that the N_(TOT) amounts of chargesequentially accumulated on the integration capacitance are the same forthe N_(TOT) beams 1520A/1520B sequentially redirected from a tile of thesame type.

In this manner, consider a sampling time t. Here, for a time T_(A)corresponding to the first pulse, a first LEE 1528 is placed in an ONstate, the other LEEs of the LEE array 1504 are maintained in an OFFstate, and the switch 1542 is in an open state. As such, the first LEE1528 illuminates with a first beam 1506 (e.g., the left-most one of thebeams 1506 in FIG. 15A or FIG. 15B) a first location of the intensitypattern 1510A/1510B, while the photo-diode 1538 captures a first beam1520A (e.g., the left-most one of the beams 1520A in FIG. 15A) or afirst beam 1520B (e.g., the top one of the beams 1520B in FIG. 15B)redirected from the first illuminated location, so the integrationcapacitance 1540 accumulates a first charge corresponding to a firstintensity of the first redirected beam, and the ADC 1544 issues a firstvalue i₁(t) for the accumulated first charge. Then, the first LEE 1528is placed in an OFF state, and the switch 1542 is placed in a closestate for a time T_(R) to reset the integration capacitance 1540. Then,for another time T_(A) corresponding to the second pulse, a second LEE1528 is placed in an ON state, the other LEEs of the LEE array 1504 aremaintained in an OFF state, and the switch 1542 is in an open state. Assuch, the second LEE 1528 illuminates with a second beam 1506 (e.g., thesecond left-most one of the beams 1506 in FIG. 15A or FIG. 15B) a secondlocation of the intensity pattern 1510A/1510B, while the photo-diode1538 captures a second beam 1520A (e.g., the second left-most one of thebeams 1520A in FIG. 15A) or a second beam 1520B (e.g., the second topone of the beams 1520B in FIG. 15B) redirected from the secondilluminated location, so the integration capacitance 1540 accumulates asecond charge corresponding to a second intensity of the secondredirected beam, and the ADC 1544 issues a second value i₂(t) for theaccumulated second charge. Then, the second LEE 1528 is placed in an OFFstate, and the switch 1542 is placed in a close state for a time T_(R)to reset the integration capacitance 1540. And so on for the remaining(N_(TOT)−2) pulses of the train associated with sampling time t. In thismanner, by the end of the (N_(TOT))^(th) pulse of the train associatedwith sampling time t, the photodetector 1522 has issued a set of “raw”intensity values {i₁(t), . . . , i_(NTOT)(t)} corresponding tointensities of the N_(TOT) redirected beams 1520A/1520B captured by thephotodetector for sampling time t.

Note that the raw intensity values {i₁(t), . . . , i_(NTOT)(t)} of theset issued by the photodetector 1522 are processed by the processor1546, so they can take only M values corresponding to the M tile typesof the intensity pattern. For the example shown in FIG. 15C, theintensity pattern 1510A/1510B has M=2 tile types, so the processor 1546obtains a set of intensity values {I₁(t), . . . , I_(NTOT)(t)} that cantake only the values I_(MAX) or I_(MIN). In some implementations, theprocessor 1546 can perform a threshold based classification on the setof raw intensity values {i₁(t), . . . , i_(NTOT)(t)}. In this case, theprocessor 1546 determines a threshold Th=(max{i₁(t), . . . ,i_(NTOT)(t)}+min{i₁(t), . . . , i_(NTOT)(t)})/2, and, for each of{I₁(t), . . . , I_(NTOT)(t)}, can set I_(j)(t)=I_(MAX) if I_(j)(t)≥Th,or I_(j)(t)=I_(MIN) if I_(j)(t)<Th, where j=1 . . . N_(TOT). As such,the processor 1546 can then determine positions of the illuminatedlocations 1508 of the intensity pattern 1510A/1510B based only onrelative differences between the intensity values {I₁(t), . . . ,I_(NTOT)(t)} of the obtained set. Hence, displacement measurementsperformed by the displacement measuring system 1500A/1500B areinsensitive to common mode drift of the LEE array 1504, for instance.

FIG. 15F shows such a set 1526(t ₀) of intensity values {I_(MIN),I_(MAX), I_(MAX), I_(MIN)} obtained by the processor 1546 based on theset of raw intensity values {i₁, i₂, i₃, i₄} issued by the photodetector1522, for sampling time t₀, corresponding to the example shown in FIG.15C. This set 1526(t ₀) of intensity values has been obtained by theprocessor 1546 because, in the example shown in FIG. 15C, the surface1511 of the binary intensity pattern 1510A/1510B is illuminated over anarea 1514 by N_(TOT)=4 beams 1506 provided by the LEE array 1504, ofwhich the two inner beams illuminate locations 1508 that are positionedon a tile of first type 1512A, and the two outer beams illuminatelocations 1508 that are positioned on respective adjacent tiles ofsecond type 1512B. In FIG. 15F, the intensity values {I_(MIN), I_(MAX),I_(MAX), I_(MIN)} of the set 1526(t ₀) are represented, by open circles,as a function of position along the x-axis of the illuminated locationsof the binary intensity pattern 1510A/1510B with which the intensityvalues are respectfully associated. Note that separation along thex-axis between adjacent illuminated locations is the known separation S.Further note that, in FIG. 15F, the intensity values {I_(MIN), I_(MAX),I_(MAX), I_(MIN)} are fit with a solid line.

Once the processor 1546 obtains, for sampling time t₀, the set 1526(t ₀)of intensity values {I_(MIN), I_(MAX), I_(MAX), I_(MIN)} shown in FIG.15F, then the processor can determine, based on additional information,that the area 1514, illuminated by the LEE array 1504 with the beams1506, spans, at t₀, over the tile borders 1513(i−1,i), 1513(i,i+1)formed between the i^(th) tile 1512A and respective adjacent (i−1)^(th),(i+1)^(th) tiles 1512B. The determined tile borders 1513(i−1,i),1513(i,i+1) can be represented, by the controller system 1525 as shownin FIG. 15F, between the appropriate positions of the illuminatedlocations with which the intensity values {I_(MIN), I_(MAX), I_(MAX),I_(MIN)} are respectfully associated.

If the intensity pattern 1510A/1510B were at rest relative to the beams1506, then instances of the set 1526(t ₁), 1526(t ₂), . . . of intensityvalues obtained by the processor 1546 at respective subsequent samplingtimes t₁, t₂, . . . would be constant in time, e.g., would be the sameas the set 1526(t ₀) obtained at sampling time t₀. However, if theintensity pattern 1510A/1510B is displaced by displacement ΔX (ordisplacement ΔY or both) relative to the beams 1506, then the instancesof the set 1526(t ₁), 1526(t ₂), . . . of intensity values obtained bythe processor 1546 at respective subsequent sampling times t₁, t₂, . . .will change in a particular manner, based on (i) a number of tile bordercrossings, and (ii) types of adjacent tiles associated with, anddirection of, each of the tile border crossings. Here, a tile bordercrossing is said to occur when the intensity pattern 1510A/1510B isdisplaced, along the x-axis, such that a tile border 1513, formedbetween a tile of first type 1512A and a tile of second type 1512B,crosses through the beam spot 1508 associated with a corresponding oneof the beams 1506. In this manner, the corresponding one of the beams1506 illuminates the tile of first type 1512A (or the tile of secondtype 1512B) before the tile border crossing and illuminates the tile ofsecond type 1512B (or the tile of first type 1512A) after the tileborder crossing, such that the tile border crossing causes a change inthe intensity of a corresponding one of the redirected beams 1520A/1520Bbetween I_(MAX) and I_(MIN).

As such, the processor 1546 can determine magnitude and direction of adisplacement ΔX of the mass 1534 along the x-axis, based on one or morechanges of the intensity values {I₁(t_(k)), . . . , I_(NTOT)(t_(k))} ofthe set 1526(t _(k)) obtained at sampling time t_(k) relative to theintensity values {I₁(t_(k+1)), I_(NTOT)(t_(k+1))} of the set 1526(t_(k+1)) obtained at a subsequent sampling time t_(k+1), where thechanges are caused by motion of the mass along the x-axis, across atleast one of the tile borders 1513. In this manner, all motion relatedspatial information for the mass 1534 is encoded in the intensitypattern 1510A/1510B. Determinations of the magnitude and direction ofdisplacements ΔX of the mass 1534 along the x-axis are described belowwhen the displacement measuring system 1500A/1500B uses the intensitypattern 1510A/1510B of FIG. 15C, or another intensity pattern 1710described in connection with FIG. 17A.

FIG. 16A shows an intensity signal that includes a sequence of sets1526(t ₀), 1626E(t₁), 1626E(t₂), 1626E(t₃) of intensity values obtainedby the processor 1546 at respective sampling times t₀, t₁, t₂, t₃ as theintensity pattern 1510A/1510B moves relative to the beams 1506, as theintensity pattern is carried in an eastward direction by the mass 1534.FIG. 16B shows another intensity signal that includes a sequence of sets1526(t ₀), 1626W(t₁), 1626W(t₂), 1626W(t₃) of intensity values obtainedby the processor 1546 at respective sampling times t₀, t₁, t₂, t₃ as theintensity pattern 1510A/1510B moves relative to the beams 1506, as theintensity pattern is carried in a westward direction by the mass 1534.Note that the starting point of each of the eastward and westwardmotions corresponds to a position of the area 1514 that includes theilluminated locations 1508, shown in FIG. 15C, when the processor 1546obtains, at sampling time t₀, the set 1526(t ₀) of intensity valuesshown in FIG. 15F and reproduced in the top panel of each of FIG. 16Aand FIG. 16B. The intensity values of the sets 1626E(t_(k)) in FIG. 16A,and the intensity values of the sets 1626W(t_(k)) in FIG. 16B, arerepresented, by open circles, as a function of position along the x-axisof the illuminated locations of the binary intensity pattern 1510A/1510Bwith which the intensity values are respectfully associated. Here,separation along the x-axis between adjacent illuminated locations isthe known separation δ.

Because the intensity pattern 1510A/1510B has a pattern period of twotiles, as it is formed from M=2 types of tiles 1512A, 1512B, and becausea width of each tile allows for N=2 concurrently illuminated locations1508, there are only M×N=4 unique sets 1626E or 1626W of intensityvalues that can be obtained by the processor 1546. In this manner, inFIG. 16A, the next set 1626E(t₄) will be equivalent to the set 1526(t₀), the next set 1626E(t₅) will be equivalent to the set 1626E(t₁), andso on a cyclical mod(M×N=4) basis. Similarly, in FIG. 16B, the next set1626W(t₄) will be equivalent to the set 1526(t ₀), the next set1626W(t₅) will be equivalent to the set 1626W(t₁), and so on a cyclicalmod(M×N=4) basis.

Also, a sampling frequency f_(S) is chosen such that, in FIG. 16A, atile border crossing in the eastward direction occurs between eachconsecutive pair of sampling points t_(k), t_(k+1); similarly, in FIG.16B, a tile border crossing in the westward direction occurs betweeneach consecutive pair of sampling points t_(k), t_(k+1). Note, however,that the set 1626E(t₂) and the set 1626W(t₂) obtained by the processor1546 at sampling time t₂ are the same, 1626E(t₂)=1626W(t₂), so theprocessor cannot unambiguously determine whether a displacement ΔX ofthe mass 1534 along the x-axis is in the eastward direction or westwarddirection based only on the set issued at this sampling time. For thisreason, the sampling rate f_(S) must be larger than 1/(t₂−t₀). Ingeneral, to unambiguously determine both the magnitude and direction ofthe displacement ΔX, the sampling rate f_(S) is chosen to satisfy thecondition f_(S)>2v_(MAX)/[δ*(N_(TOT)−1)], if a period P of the intensitypattern 1510A/1510B satisfies the condition P>δ*(N_(TOT)−1); or thesampling rate f_(S) is chosen to satisfy the condition f_(S)>2v_(MAX)/P,if the period P of the intensity pattern satisfies the conditionP≤δ*(N_(TOT)−1). Here, v_(MAX) is the maximum velocity of the mass 1534,and δ is the separation between the illuminated locations 1508. Notethat the above conditions hold only when δ>0, which is always true forN_(TOT)≥2. For the example illustrated in FIG. 15C, N_(TOT)=4, and theperiod P of the intensity pattern 1510A/1510B, which is equal to a sumof the width of the first type tile 1512A and the width of the secondtype tile 1512B, is larger than δ*3. As such, in this example, thesampling frequency f_(S) satisfies f_(S)>2v_(MAX)/(3*δ).

In some implementations, sets 1626E(t_(k)) of intensity values shown inFIG. 16A and sets 1626W(t_(k)) of intensity values shown in FIG. 16B,for k=0, 1, 2, . . . , can be deemed as sets of expected intensityvalues corresponding to particular positions along the x-axis ofilluminated locations of the intensity pattern 1510A/1510B. In suchcases, a first mapping of the sets 1626E(t_(k)) of expected intensityvalues shown in FIG. 16A to the particular positions along the x-axis ofilluminated locations of the intensity pattern 1510A/1510B can berecorded in a data store, e.g., in a register, a lookup table, etc.Similarly, a second mapping of the sets 1626W(t_(k)) of expectedintensity values shown in FIG. 16B to the particular positions along thex-axis of illuminated locations of the intensity pattern 1510A/1510B canbe recorded in the data store. In these implementations, the processor1546 uses an obtained set of intensity values (e.g., 1626W(t₃)) againstthe second mapping of the sets 1626W(t_(k)) of expected intensity valuesto positions of illuminated locations of the intensity pattern1510A/1510B (e.g., as shown in FIG. 16B), to determine a position on theintensity pattern of the area 1514 that includes the illuminatedlocations 1508 (e.g., two left beams illuminate a tile of first type1512A between tile borders 1513(i−3,i−2), 1513(i−2,i−1), and two rightbeams illuminate a tile of second type 1512B between tile borders1513(i−2,i−1), 1513(i−1,i), as shown in the fourth panel of FIG. 16B).

As noted above, even if the LEE array 1504 were replaced with a singleLEE 1528, the displacement measuring system 1500A/1500B would still becapable of resolving both direction and magnitude of the displacement ΔXof the mass 1534 along the x-axis, as long as the intensity patterns1510A/1510B were replaced with an intensity pattern with M≥3 tile types.FIG. 17A is a plan view in the (x,y) plane of surface 1511 of such anintensity pattern 1710 that has M=3 tile types: tiles of first type1712A, tiles of second type 1712B and tiles of third type 1712C, where atile of first type 1712A forms a tile border 1713AB with a tile ofsecond type 1712B and a tile border 1713AC with a tile of third type1712C, and a tile of second type 1712B forms a tile border 1713BC with atile of third type 1712C. A tile of first type 1712A is configured suchthat, when a single beam (e.g., only the left-most one from among thebeams 1506 depicted in FIG. 15A or FIG. 15B) illuminates it, the singlebeam 1520A (e.g., only the left-most one of the beams 1520A depicted inFIG. 15A) or the single beam 1520B (e.g., only the top one of the beams1520B depicted in FIG. 15B) has a maximum intensity I_(A). Further, atile of third type 1712C is configured such that, when the single beam1506 illuminates it, the single redirected beam 1520A/1520B has aminimum intensity I_(C), where I_(C)<I_(A). Furthermore, a tile ofsecond type 1712B is configured such that, when the single beam 1506illuminates it, the single redirected beam 1520A/1520B has anintermediate intensity I_(B), where I_(C)<I_(B)<I_(A). Here, the tileborders 1713AB, 1713AC, 1713BC are distributed at known locationsrelative to each other along the x-axis, so the intensity pattern 1710can be used as part of the displacement measuring system 1500A/1500B tomeasure displacement ΔX of the mass 1534 along the x-axis.

In the implementations of the displacement measuring system 1500A/1500Bthat uses a single LEE 1528 in conjunction with the intensity pattern1710, the switching gate 1524, that is used by the PWM driver 1536 fortiming acquisition of raw intensity values issued by the photodetector1522, is modified such that each train includes a single pulse, suchthat the modified timing gate is a sequence of pulses repeated in timewith a period T_(S). Here, the pulses of the modified timing gatecorrespond to sampling times t₀, t₁, t₂, and so on. In this manner, at asampling time t, the LEE 1528 is placed in an ON state for a time T_(A)corresponding to the pulse length, and the switch 1542 is in an openstate. As such, the LEE 1528 illuminates with a single beam a singlelocation 1708 of the intensity pattern 1710, while the photo-diode 1538captures a beam redirected from the illuminated location 1708, so theintegration capacitance 1540 accumulates a charge corresponding to anintensity of the redirected beam 1520A/1520B, and the ADC 1544 issues asingle value i(t) for the accumulated charge. Then, the single LEE 1528is placed in an OFF state, and the switch 1542 is placed in a closestate for a time T_(S) corresponding to the sampling period. In thismanner, the photodetector 1522 has issued a single “raw” intensity valuei(t) corresponding to the intensity of the single redirected beam1520A/1520B captured by the photodetector for sampling time t.

The raw intensity value i(t) issued by the photodetector 1522 isprocessed by the processor 1546, so it can take only M valuescorresponding to the M tile types of the intensity pattern. For theexample shown in FIG. 17A, the intensity pattern 1710 has M=3 tiletypes, so the processor 1546 obtains a single intensity value I(t) thatcan take only the values I_(A), I_(B) or I_(C). In this example, theprocessor 1546 can perform a threshold based classification on the rawintensity value i(t) using two thresholds Th_(AB) and Th_(BC). Here, theprocessor 1546 can set I(t)=I_(A) if I(t)≥Th_(AB), or I(t)=I_(C) ifI(t)≤Th_(BC), or I(t)=I_(B) if Th_(BC)<I(t)<Th_(AB). If the intensitypattern 1710 is displaced by displacement ΔX relative to the singlebeams 1506, then intensity values I(t₀), I(t₁), I(t₂), . . . obtained bythe processor 1546 at respective subsequent sampling times t₀, t₁, t₂, .. . will change in a particular manner, based on (i) a number of tileborder crossings, and (ii) types of adjacent tiles associated with, anddirection of, each of the tile border crossings. As such, the processor1546 can determine magnitude and direction of a displacement ΔX of themass 1534 along the x-axis, based on a change of the intensity valueI(t_(k)) obtained at sampling time t_(k) relative to the intensity valueI(t_(k+1)) obtained at a subsequent sampling time t_(k+1), where thechange is caused by motion of the mass along the x-axis, across at leastone of the tile borders 1713AB, 1713AC or 1713BC. In this manner, allmotion related spatial information for the mass 1534 is encoded in theintensity pattern 1710. Determinations of the magnitude and direction ofdisplacements ΔX of the mass 1534 along the x-axis are described belowin connection with FIGS. 17B and 17C.

FIG. 17B shows an intensity signal that includes a sequence of intensityvalues I(t₀), I_(E)(t₁), I_(E)(t₂) obtained by the processor 1546 atrespective sampling times t₀, t₁, t₂ as the intensity pattern 1710 movesrelative to the single beam 1506, as the intensity pattern is carried inan eastward direction by the mass 1534. FIG. 17C shows another intensitysignal that includes a sequence of intensity values I(t₀), I_(W)(t₁),I_(W)(t₂) obtained by the processor 1546 at respective sampling timest₀, t₁, t₂ as the intensity pattern 1710 moves relative to the singlebeam 1506, as the intensity pattern is carried in a westward directionby the mass 1534. Note that the starting point of each of the eastwardand westward motions corresponds to position of the illuminated location1708, shown in FIG. 17A, when the processor 1543 issues, at samplingtime t₀, the intensity value I(t₀)=I_(A) shown in the top panel of eachof FIG. 17B and FIG. 17C. The intensity values I_(E)(t_(k)) in FIG. 17B,and the intensity values I_(W)(t_(k)) in FIG. 17C are represented, byopen circles, as a function of positions along the x-axis of theilluminated location of the intensity pattern 1710 with which theintensity values are respectfully associated. Here, the tiles arecounted, starting from 0 at the center tile, as tiles+1, +2, . . . goingeastward, and as tiles−1, −2, . . . going westward.

Because the intensity pattern 1710 has a pattern period of three tiles,as it is formed from M=3 types of tiles 1712A, 1712B, 1712C and becausethere is no more than N=1 illuminated location 1708 per tile, there areonly M×N=3 unique intensity values I_(E)(t_(k)) or I_(W)(t_(k)) that canbe obtained by the processor 1546. In this manner, in FIG. 17B, the nextintensity value I_(E)(t₃) will be equivalent to the intensity valueI(t₀), the next intensity value I_(E)(t₄) will be equivalent to theintensity value I_(E)(t₁), and so on a cyclical mod(M×N=3) basis.Similarly, in FIG. 17C, the next intensity value I_(W)(t₃) will beequivalent to the intensity value I(t₀), the next intensity valueI_(W)(t₄) will be equivalent to the intensity value I_(W)(t₁), and so ona cyclical mod(M×N=3) basis.

Also, a sampling frequency f_(S) is chosen such that, in FIG. 17B, atile border crossing in the eastward direction occurs between eachconsecutive pair of sampling points t_(k), t_(k+1); similarly, in FIG.17C, a tile border crossing in the westward direction occurs betweeneach consecutive pair of sampling points t_(k), t_(k−1). As such, inthis case, to unambiguously determine both the magnitude and directionof the displacement ΔX, the sampling rate f_(S) is chosen to satisfy thecondition f_(S)>2Mv_(MAX)/P, where v_(MAX) is the maximum velocity ofthe mass 1534, and P is the period of an intensity pattern with M typesof tiles. For the example illustrated in FIG. 17A in which N_(TOT)=1,the number of tile types is M=3, and the period P of the intensitypattern 1710 is equal to a sum of the width of the first type tile1712A, the width of the second type tile 1712B, and the width of thethird type tile 1712C. As such, in this example, the sampling frequencyf_(S) satisfies f_(S)>6v_(MAX)/P.

In some implementations, intensity values I_(E)(t_(k)) shown in FIG. 17Band intensity values I_(W)(t_(k)) shown in FIG. 17C, for k=0, 1, 2 canbe deemed as expected intensity values corresponding to particularpositions along the x-axis of the illuminated location of the intensitypattern 1710. In such cases, a first mapping of expected intensityvalues I_(E)(t_(k)) shown in FIG. 17B to the particular positions alongthe x-axis of an illuminated location of the intensity pattern 1710 canbe recorded in a data store, e.g., in a register, a lookup table, etc.Similarly, a second mapping of expected intensity values I_(W)(t_(k))shown in FIG. 17C to the particular positions along the x-axis of anilluminated location of the intensity pattern 1710 can be recorded inthe data store. In these implementations, the processor 1546 uses anobtained intensity value (e.g., I_(W)(t₂)) against the second mapping ofthe expected intensity values I_(W)(t_(k)) to positions of anilluminated location of the intensity pattern 1710 (e.g., as shown inFIG. 17C), to determine a position on the intensity pattern of theilluminated location 1708 (e.g., the single beam 1506 illuminates a tileof third type 1712C between the tile border 1713(+1,+2) and the tileborder 1713(+2,+3), as shown in the third panel of FIG. 17C).

The intensity patterns 1510A/1510B, 1710 described above, having a 1Dprofile, can be used by the displacement measuring system 1500A/1500B toperform measurements of displacement ΔX along a single direction. Someof the components of the displacement measuring system 1500A/1500B canbe modified, as described below, to allow for concurrently measuring thedisplacement ΔX of the mass along the x-axis, e.g., corresponding tovibration left-and-right on page, and the displacement ΔY of the massalong the y-axis, e.g., corresponding to vibration in-and-out of page.

FIG. 18A is a zoomed-in view in the (x,z) plane of a portion of thedisplacement measuring system 1500A/1500B that shows a modified LEEarray 1804 and a portion of a modified intensity pattern 1810 attachedto the surface of the mass 1534 facing the LEE array. The LEE array 1804is spaced apart from the intensity pattern 1810 and outputs N_(TOT)beams 1806 that illuminate the surface 1511 of the intensity pattern.FIG. 18B is a plan view in the (x,y) plane of the LEE array 1804. TheLEE array 1804 includes a board 1803 and LEEs 1828 distributed in rowsalong the x-axis, each row having N_(X) LEEs, and columns along they-axis, each column having N_(Y) LEEs. The LEEs 1828 respectivelyprovide the beams 1806 used to illuminate the intensity pattern 1810. Inthis example, parameters of the LEE array 1804 are N_(TOT)=4, N_(X)=2,N_(Y)=2. In some implementations, the LEEs 1828 can be the same as theLEEs 1528 described above in connection with FIGS. 15A-15D, and can betime multiplexed using a timing gate like the timing 1524 shown in FIG.15E.

FIG. 18C is a plan view in the (x,y) plane of surface 1511 of themodified intensity pattern 1810. In this example, the intensity pattern1810 has M=4 tile types: tiles of first type 1812A, tiles of second type1812B, tiles of third type 1812C and tiles of fourth type 1812D. A tileof first type 1712A is configured such that, when one of the beams 1806illuminates it, the corresponding one of the redirected beams1520A/1520B has a maximum intensity I_(A). Further, a tile of fourthtype 1712D is configured such that, when one of the beams 1806illuminates it, the corresponding one of the redirected beams1520A/1520B has a minimum intensity I_(D), where I_(D)<I_(A).Furthermore, a tile of second type 1812B is configured such that, whenone of the beams 1806 illuminates it, the corresponding one of theredirected beams 1520A/1520B has a first intermediate intensity I_(B).Also, a tile of third type 1812C is configured such that, when one ofthe beams 1806 illuminates it, the corresponding one of the redirectedbeams 1520A/1520B has a second intermediate intensity I_(C). In general,the intensities I_(A), I_(D), I_(C), and I_(B) can have any values aslong as they are different from each other. Also, the separation betweenthe values of the intensities I_(A), I_(D), I_(C), and I_(B) also needsto be sufficiently large to ensure sufficient signal to noise ratio(SNR) for level detection. In the example illustrated in FIG. 18C, thevalues of the intensities I_(A), I_(D), I_(C), and I_(B) satisfy thefollowing conditions, I_(D)<I_(C)<I_(B)<I_(A), as an illustrativeexample.

Moreover, tiles of first type 1812A and tiles of second type 1812B areseparated by tile borders 1813AB, oriented along the x-axis; tiles offirst type 1812 and tiles of third type 1812C are separated by tileborders 1813AC, oriented along the y-axis; tiles of second type 1812Band tiles of fourth type 1812D are separated by tile borders 1813BD,oriented along the y-axis; and tiles of third type 1812C and tiles offourth type 1812D are separated by tile borders 1813CD, oriented alongthe x-axis. In this manner, the tiles are arranged such that each corner1850 of each tile is a corner that is shared by the tile with threeother tiles of different type. The tile borders 1813AC, 1813BD aredistributed at known locations relative to each other along the x-axis,and the tile borders 1813AB, 1813CD are distributed at known locationsrelative to each other along the y-axis, so the intensity pattern 1810can be used as part of the displacement measuring system 1500A/1500B toconcurrently measure displacement ΔX of the mass 1534 along the x-axisand displacement ΔY of the mass along the y-axis.

Further in the example shown in FIG. 18C, the LEE array 1804 illuminatesan area 1814 of the intensity pattern 1810 with N_(TOT)=4 beams 1806,such that a separation between the illuminated locations 1808 is a firstseparation δ_(X) along the x-axis, and a second separation δ_(Y) alongthe y-axis. In some implementations, the first separation δ_(X) and thesecond separation δ_(Y) are equal, δ_(X)=δ_(Y)=δ. Furthermore, in theexample shown in FIG. 18C, a size along each of the x-axis and y-axis ofeach of tiles 1812A, 1812B, 1812C, 1812D can accommodate an N=2concurrently illuminated locations 1808. In this manner, the processor1546 (in conjunction with the photodetector 1522 of the displacementmeasuring system 1500A/1500B) obtains, for each sampling time t_(k), aset of N_(TOT)=4 intensity values corresponding to intensities ofrespective beams 1520A/1520B redirected from the area 1814 of theintensity pattern 1810 that includes the illuminated locations 1806.

In some implementations, the surface 1511 of the intensity pattern 1810can be configured as a reflective surface that selectively reflects,scatters or both the illuminating beams 1806 to the photodetector 1522as redirected beams 1520A, as described in detail in connection withFIG. 15A and FIG. 15C. In other implementations, the intensity pattern1810 can be configured as a combination of a transmissive surface 1511,an array of micro-mirrors 1518 (or micro-prisms, or other redirectingmicro-structures), and a transmissive surface 1516, as described indetail in connection with FIG. 15B and FIG. 15C. In this manner, thetransmissive surface 1511 selectively transmits the illuminating beams1806, the array of micro-mirrors 1518 reflects, scatters or both theselectively transmitted beams, and the transmissive surface 1516transmits the redirected beams 1520B to the photodetector 1522, asexplained in connection with FIG. 15B.

Referring again to the example shown in FIG. 18C, at sampling time t₀,an area 1814 of the intensity pattern 1810 is positioned across fourtile borders 1813AB, 1813AC, 1813CD, 1813BD (or equivalently straddle acorner 1850), such that a corresponding one of the four illuminatedlocations 1808 lies on each one of the four adjacent tiles 1812A, 1812C,1812D, 1812B that form the concurrently crossed tile borders. As such, aset 1826(t ₀) obtained by the processor 1546 includes the intensityvalues {I_(A), I_(C), I_(D), I_(B)} corresponding to quadrants I, II,III, IV, respectively, of area 1814. The intensity pattern 1810 can bemoved along with the mass 1534 relative to the four beams 1806, based onan axial motion vector 1852, along the x-axis or the y-axis. When theintensity pattern 1810 is moved eastward along the axial motion vector1852 illustrated in FIG. 18C, at sampling time t₁, the area 1814 ispositioned across a single tile border 1813CD, such that a row of thefour illuminated locations 1808 lies on each of the adjacent tiles1812C, 1812D that form the crossed tile border. As such, a set 1826E(t₁)obtained by the processor 1546 includes the intensity values {I_(C),I_(C), I_(D), I_(D)} corresponding to quadrants I, II, III, IV,respectively, of area 1814. When the intensity pattern 1810 is movedfurther eastward along axial motion vector 1852, at sampling time t₂,the area 1814 is positioned across four tile borders 1813CD, 1813AC,1813AB, 1813BD, such that a corresponding one of the four illuminatedlocations 1808 lies on each one of the four adjacent tiles 1812C, 1812A,1812B, 1812D that form the concurrently crossed tile borders. As such, aset 1826E(t₂) obtained by the processor 1546 includes the intensityvalues {I_(C), I_(A), I_(B), I_(D)} corresponding to quadrants I, II,III, IV, respectively, of area 1814. FIG. 18D shows an intensity signalthat includes the sequence of sets 1826(t ₀), 1826E(t₁), 1826E(t₂)obtained by the processor 1546 at respective sampling times t₀, t₁, t₂as the intensity pattern 1810 moves relative to the beams 1806, as theintensity pattern 1810 is carried in the eastward direction by the mass1534. The intensity values of the sets 1826E(t_(k)) in FIG. 18D arerepresented, as a grey-level inside circles, as a function of positionin the (x,y) plane of the illuminated locations of the intensity pattern1810 with which the intensity values are respectfully associated. Here,separation along the x-axis and the y-axis between adjacent illuminatedlocations is the known separation δ.

Referring again to FIG. 18C, note that, at sampling time t₂, the sameset 1826E(t₂) would be obtained by the processor 1546 if the intensitypattern 1810 were moved in a westward, opposing motion vector 1852. Assuch, to unambiguously determine the direction of motion, the samplingfrequency has to be larger than 1/(t₂−t₀).

Referring again to FIG. 18C, the intensity pattern 1810 can be movedalong with the mass 1534 relative to the four beams 1806 based on adiagonal motion vector 1854. When the intensity pattern 1810 is moved ina NE direction along the diagonal motion vector 1854 illustrated in FIG.18C, at sampling time t₁, the area 1814 is inscribed in a single tile1812D, so it does not cross any tile border. As such, a set 1826NE(t₁)obtained by the processor 1546 includes the intensity values {I_(D),I_(D), I_(D), I_(D)} corresponding to quadrants I, II, III, IV,respectively, of area 1814. When the intensity pattern 1810 is movedfurther in the NE direction along diagonal motion vector 1854, atsampling time t₂, the area 1814 is positioned across four tile borders1813CD, 1813BD, 1813AB, 1813AC, such that a corresponding one of thefour illuminated locations 1808 lies on each one of the four adjacenttiles 1812D, 1812B, 1812A, 1812C that form the concurrently crossed tileborders. As such, a set 1826NE(t₂) obtained by the processor 1546includes the intensity values {I_(D), I_(B), I_(A), I_(C)} correspondingto quadrants I, II, III, IV, respectively, of area 1814.

Note that, at sampling time t₂, the same set 1826E(t₂) of intensityvalues would be obtained by the processor 1546 if the intensity pattern1810 were moved in westward, opposing axial motion vector 1852. Also atsampling time t₂, the same set 1826NE(t₂) of intensity values would beissued by the photodetector 1522 if the intensity pattern 1810 weremoved in a southwest direction, opposing diagonal motion vector 1854. Assuch, to unambiguously determine the direction of motion, the samplingfrequency has to satisfy the following condition: f_(S)>1/(t₂−t₀).

As such, FIG. 18E shows a first group 1856 of unique sets 1826 ofexpected intensity values corresponding to particular positions in the(x,y) plane of illuminated locations of the intensity pattern 1810,where each of the sets of the first group 1856 can be used by theprocessor 1546 to unambiguously determine the absolute value anddirection of displacements ΔX and ΔY of the intensity pattern relativeto the beams 1810. FIG. 18E also shows a second group 1858 of non-uniquesets 1826 of expected intensity values corresponding to particularpositions in the (x,y) plane of illuminated locations of the intensitypattern 1810. While the sets 1826 of intensity values of the secondgroup 1858 can be used by the processor 1546 to determine the absolutevalue of displacements ΔX and ΔY of the intensity pattern relative tothe beams 1810, respective directions of the displacements ΔX and ΔY canbe one of multiple possible directions. However, the sets 1826 ofintensity values of the second group 1858 can be used for errorcorrection, e.g., to detect motion aliasing when the mass 1534supporting the intensity pattern 1810 is moving too fast or the samplingrate f_(S) is too slow.

In some implementations, at least the first group 1856 of unique sets1826 of intensity values corresponding to particular positions in the(x,y) plane of illuminated locations of the intensity pattern 1810 canbe recorded in a data store, e.g., in a register, a lookup table, etc.In these implementations, the processor 1546 uses an obtained set ofintensity values (e.g., 1826E(t₁)) against the recorded first group 1856of the sets 1826 of expected intensity values corresponding toparticular positions in the (x,y) plane of illuminated locations of theintensity pattern 1810 (e.g., as shown in FIG. 18E), to determine aposition on the intensity pattern of the area 1814 that includes theilluminated locations 1808 (e.g., a row of two beams illuminate a tileof third type 1812C and, across the tile border 1813CD, a row of twobeams illuminate a tile of fourth type 1812D, as shown in the secondpanel of FIG. 18D).

FIG. 19A shows an intensity pattern 1910 that is misaligned relative tothe LEE array 1504 of the displacement measuring system 1500A/1500B,e.g., rotated relative to the x-axis and y-axis by a rotation angle θ.This misalignment can be compensated for by sweeping over the fullΔX_(MAX) motion range and measuring the corresponding displacementΔY_(MEAS) over this range to estimate θ. Such a misalignmentcompensation can be performed at fabrication time, or in the field. Forexample, while a device carrying the displacement measuring system1500A/1500B is charging, it can be verified whether there is amisalignment of the intensity pattern 1910 pattern to the LEE array1504. The processor 1546 determines the angular misalignment θ based onthe known ΔX_(MAX) motion range and measured displacement ΔY_(MEAS).Once the angular misalignment θ is determined, the processor 1546transforms the intensity pattern 1910 using a rotation matrix todetermine a scaling factor [1/cos(θ)]. FIG. 19B shows that adisplacement ΔX measured by the displacement measuring system1500A/1500B using the rotated intensity pattern 1910 will be scaled bythe processor 1546, based on the determined scaling factor, to outputthe “true” displacement as a scaled displacement ΔX_(S). A magnitude ofscaled displacement ΔX_(S) is larger than a magnitude of the measureddisplacement ΔX based on the determined scaled factor: ΔX_(S)=ΔX/cos(θ).

The displacement measuring system 1500A/1500B in conjunction withintensity patterns 1510A/1510B, 1710 and 1810 can be used to measureangular displacement in various rotational configurations, as describedbelow.

FIG. 20A is a side view, in the (y,z) plane, of a first example of anangular displacement measuring system 2000 configured to measure angulardisplacement Δθ of a wheel 2034. Here, a device 2030 has a frame 2032that encapsulates at least a portion of the angular displacementmeasuring system 2000 and a portion of the wheel 2034. A remainingportion of the wheel 2034 protrudes outside of the frame 2032 throughslot 2033, for instance. In some implementations, the device 2030 is awatch, and the wheel 2034 is a setting/control crown.

In this example, the angular displacement measuring system 2000 is amodification of the displacement measuring system 1500B described abovein connection with FIG. 15B. The angular displacement measuring system2000 includes the mount 1502B, the LEE array 1504, and the photodetector1522, all of which described in detail above in connection with FIGS.15B-15E. Note that the N_(TOT) LEEs 1528 of the LEE array 1504 aredistributed along the x-axis.

An intensity pattern 2010 of the angular displacement measuring system2000 is a structure shaped like a wheel that is disposed co-axially withthe wheel 2034 and is coupled with a side wall surface 2035XY of thewheel 2034. A side wall surface 2011 of the intensity pattern 2010 isspaced apart from and faces the LEE array 1504, and a rim surface 2016of the intensity pattern 2010 is spaced apart from and faces thephotodetector 1522. In this manner, during operation of the angulardisplacement measuring system 2000, the LEE array 1504 illuminates atransmissive side wall surface 2011 of the intensity pattern 2010 withN_(TOT) beams 1506, and the intensity pattern redirects, through itstransmissive rim surface 2016 to the photodetector 1522, at least someof the light impinging on the illuminated surface, such that N_(TOT)redirected beams 1520B form a folding angle relative the illuminatingbeams. In some cases, the folding angle formed by the redirected beams1520B relative the illuminating beams 1506 can be a substantially rightangle. In the example illustrated in FIG. 20A, the intensity pattern2010 includes an array of micro-mirrors 2018 (or micro-prisms, or otherredirecting micro-structures) between the transmissive side wall surface2011 and the transmissive rim surface 2016. Here, the flat surface ofthe micro-mirrors of the array 2018 is oriented parallel to the x-axis.In this manner, the transmissive side wall surface 2011 selectivelytransmits the illuminating beams 1506, the array of micro-mirrors 2018reflects, scatters or both the selectively transmitted beams, and thetransmissive rim surface 2016 transmits the redirected beams 1520B tothe photodetector 1522.

FIG. 20B is a plan view in the (x,y) plane of side wall surface 2011 ofthe intensity pattern 2010. In this example, the intensity pattern 2010has M=2 tile types: tiles of first type 2012A and tiles of second type2012B separated from each other by tile borders 2013. Note that thetiles 2012A, 2012B are shaped as annulus sectors. A tile of first type2012A is configured such that, when one of the beams 1506 illuminatesit, the corresponding one of the redirected beams 1520B has a maximumintensity I_(MAX). Further, a tile of second type 2012B is configuredsuch that, when one of the beams 1506 illuminates it, the correspondingone of the redirected beams 1520B has a minimum intensity I_(MIN), whereI_(MIN)<I_(MAX). Here, the tile borders 2013 are distributed at knownangular locations relative to each other along the azimuthal θ-axis, sothe intensity pattern 2010 can be used as part of the angulardisplacement measuring system 2000 to measure an angular displacement Δθof the wheel 2034 along the azimuthal θ-axis. Further in the exampleshown in FIGS. 20A-20B, the LEE array 1504 illuminates an area 1514 ofside wall surface 2011 of the intensity pattern 2010 with N_(TOT) beams1506, and a separation between the illuminated locations 1508 is a knownseparation δ. Moreover, the size along the azimuthal θ-axis of each oftiles 2012A, 2012B can accommodate 1≤N≤N_(TOT) concurrently illuminatedlocations 1508.

In this manner, the PWM driver 1536 of the angular displacementmeasuring system 2000 can use a switching gate, similar to the switchinggate 1524 shown in FIG. 15E, to time multiplex the N_(TOT) LEEs 1528 ofthe LEE array 1504. In this manner, the processor 1546 (in conjunctionwith the photodetector 1522) obtains, for each sampling time t_(k), anassociated set of N_(TOT) intensity values corresponding to intensitiesof respective beams 1520B redirected by the intensity pattern 2010 viatransmission through the side wall surface 2011 at the illuminatedlocations 1508. As such, the processor 1546 of the angular displacementmeasuring system 2000 can determine, for each sampling time t_(k),positions along the azimuthal θ-axis of the illuminated locations 1508of the side wall surface 2011 of the intensity pattern 2010 based onrelative differences between the intensity values of the associatedissued set. Then, in a manner similar to the manners described above inconnection with FIG. 16A-16B or 17B-17C (e.g., by substituting ΔX withΔθ), the processor 1546 determines, for each sampling time t_(k), anangular displacement Δθ of the wheel 2034 based on one or more changesof the intensity values of the obtained set caused by rotation of thewheel that sweeps at least one of the tile borders 2013 through at leastone of the illuminating beams 1506.

FIG. 21A is a side view, in the (y,z) plane, of a second example of anangular displacement measuring system 2100A or a third example of anangular displacement measuring system 2100B each configured to measureangular displacement Δθ of a wheel 2134. Here, a device 2130 has a frame2132 that encapsulates at least a portion of one of the angulardisplacement measuring systems 2100A, 2100B and a portion of the wheel2134. A remaining portion of the wheel 2134 protrudes outside of theframe 2132 through slot 2133, for instance. In some implementations, thedevice 2130 is a watch, and the wheel 2134 is a setting/control crown.

In this example, the angular displacement measuring system 2100A is amodification of the displacement measuring system 1500A described abovein connection with FIG. 15A, and the angular displacement measuringsystem 2100B is a modification of the displacement measuring system1500B described above in connection with FIG. 15B. The angulardisplacement measuring system 2100A/2100B includes the mount1502A/1502B, the LEE array 1504, and the photodetector 1522A/1522B, allof which described in detail above in connection with FIGS. 15A-15E.Note that the N_(TOT) LEEs 1528 of the LEE array 1504 are distributedalong the x-axis.

An intensity pattern 2110 of the angular displacement measuring system2100A/2100B is a structure shaped like a wheel that is disposedco-axially with the wheel 2134 and coupled with a side wall surface2135YZ of the wheel 2134. FIG. 21B is a plan view in the (x,z) plane ofthe side wall surface 2116 of the intensity pattern 2110 that is distalfrom the side wall surface 2135YZ of the wheel 2134. In the exampleillustrated in FIGS. 21A-21B, the intensity pattern 2110 includes anarray of micro-mirrors 2118 (or micro-prisms, or other redirectingmicro-structures) between a transmissive rim surface 2111 and atransmissive side wall surface 2116. Here, the flat surface of themicro-mirrors of the array 2118 is oriented parallel to the y-axis. Insome implementations, the transmissive rim surface 2111 is configured asthe surface 1511 of the intensity pattern 1510A/1510B described above inconnection with FIG. 15C. In other implementations, the transmissive rimsurface 2111 is configured as the surface 1511 of the intensity pattern1710 described above in connection with FIG. 17A. In some otherimplementations, the transmissive rim surface 2111 is configured as thesurface 1511 of the intensity pattern 1810 described above in connectionwith FIG. 18C. In either of these implementations, the tile borders 1513or 1713 or the tile borders 1813 along the y-axis are distributed atknown angular locations relative to each other along the azimuthalθ-axis, so the intensity pattern 2110 can be used as part of the angulardisplacement measuring system 2100A/2100B to measure an angulardisplacement Δθ of the wheel 2134 along the azimuthal θ-axis.

For the angular displacement measuring system 2100A, the rim surface2111 of the intensity pattern 2110 is spaced apart from and faces theLEE array 1504 and the photodetector 1522A. In this manner, duringoperation of the angular displacement measuring system 2100A, the LEEarray 1504 illuminates the transmissive rim surface 2111 of theintensity pattern 2110 with N_(TOT) beams 1506; the transmissive rimsurface 2111 selectively transmits the N_(TOT) beams 1506; the array ofmicro-mirrors 2118 reflects, scatters or both the selectivelytransmitted beams, such that N_(TOT) redirected beams 1520A form anacute angle relative the selectively transmitted beams; and the rimsurface 2111 transmits the redirected beams 1520A to the photodetector1522A. In another implementation of the angular displacement measuringsystem 2100A (not illustrated in FIG. 21B), the intensity pattern 2110is configured to have a selectively reflective rim surface 2111 asdescribed above in connection with FIG. 15C, FIG. 17A or FIG. 18C.During operation of this implementation of the angular displacementmeasuring system 2100A, the LEE array 1504 illuminates the reflectiverim surface 2111 of the intensity pattern 2110 with N_(TOT) beams 1506;and the reflective rim surface 2111 selectively redirects (viareflection, scattering or both) the N_(TOT) beams 1506 to thephotodetector 1522A, such that the N_(TOT) redirected beams 1520A forman acute angle relative the beams 1506.

For the angular displacement measuring system 2100B, the rim surface2111 of the intensity pattern 2110 is spaced apart from and faces theLEE array 1504, and the side wall surface 2116 of the intensity pattern2110 is spaced apart from and faces the photodetector 1522B. In thismanner, during operation of the angular displacement measuring system2100B, the LEE array 1504 illuminates the transmissive rim surface 2111of the intensity pattern 2110 with N_(TOT) beams 1506; the transmissiverim surface 2111 selectively transmits the N_(TOT) beams 1506; the arrayof micro-mirrors 2118 reflects, scatters or both the selectivelytransmitted beams, such that N_(TOT) redirected beams 1520B form afolding angle relative the selectively transmitted beams (e.g., thefolding angle formed by the redirected beams 1520B relative theilluminating beams 1506 can be a substantially right angle); and thetransmissive side wall surface 2116 transmits the redirected beams 1520Bto the photodetector 1522B.

Further in the example shown in FIGS. 21A-21B, the LEE array 1504illuminates an area 1514 of the rim surface 2111 of the intensitypattern 2110 with N_(TOT) beams 1506, and a separation between theilluminated locations 1508 is a known separation S. Moreover, the sizealong the azimuthal θ-axis of each of tiles 1512 or 1712 or 1812 canaccommodate 1≤N≤N_(TOT) concurrently illuminated locations 1508.

In this manner, the PWM driver 1536 of the angular displacementmeasuring system 2100A/2100B can use a switching gate, similar to theswitching gate 1524 shown in FIG. 15E, to time multiplex the N_(TOT)LEEs 1528 of the LEE array 1504. In this manner, the processor 1546 (inconjunction with the photodetector 1522A/1522B) obtains, for eachsampling time t_(k), an associated set of N_(TOT) intensity valuescorresponding to intensities of respective beams 1520A/1520B redirectedby the intensity pattern 2110 via either reflection off a selectivelyreflective rim surface 2111 at the illuminated locations 1508, ortransmission through a selectively transmissive rim surface 2111 at theilluminated locations 1508. As such, the processor 1546 of the angulardisplacement measuring system 2100A/2100B can determine, for eachsampling time t_(k), positions along the azimuthal θ-axis of theilluminated locations 1508 of the rim surface 2111 of the intensitypattern 2110 based on relative differences between the intensity valuesof the associated issued set. Then, in a manner similar to the mannersdescribed above in connection with FIGS. 16A-16B or FIGS. 17B-17C orFIGS. 18C-18E (e.g., by substituting ΔX with Δθ), the processor 1546determines, for each sampling time t_(k), an angular displacement Δθ ofthe wheel 2134 based on one or more changes of the intensity values ofthe obtained set caused by rotation of the wheel that sweeps at leastone of the tile borders 1513 or 1713 or the tile borders 1813 along they-axis through at least one of the illuminating beams 1506.

FIG. 22A is a side view, in the (y,z) plane, of another example of adisplacement measuring system 2200 configured to concurrently measureangular displacement Δθ and axial displacement ΔY of a wheel 2235. Here,a device 2230 has a frame 2232 that encapsulates at least a portion ofthe displacement measuring system 2200 and a portion of an axle 2234 onwhich the wheel 2235 is mounted. A remaining portion of the axle 2234protrudes outside of the frame 2232 through an opening 2233 with bearingmechanism, for instance. In some implementations, the device 2230 is awatch, and the wheel 2235 is a setting/control crown.

In this example, the displacement measuring system 2200 is amodification of the displacement measuring system 1500A described abovein connection with FIG. 15A and FIGS. 18A-18B. The displacementmeasuring system 2200 includes the mount 1502A, the LEE array 1804, andthe photodetector 1522, all of which described in detail above inconnection with FIGS. 15A-15E and FIGS. 18A-18B. Note that the N_(TOT)LEEs 1828 of the LEE array 1804 are distributed in N_(X) rows along thex-axis and N_(Y) rows along the y-axis.

An intensity pattern 2210 of the displacement measuring system 2200 is astructure shaped like a wheel that is disposed on a rim surface 2262 ofthe axle 2234, i.e., co-axially with the wheel 2235. FIG. 22B is a planview in the (x,z) plane of one of the two side wall surfaces 2216 of theintensity pattern 2210. In the example illustrated in FIGS. 22A-22B, theintensity pattern 2210 includes an array of micro-mirrors 2218 (ormicro-prisms, or other redirecting micro-structures) between atransmissive rim surface 2211 and the side wall surfaces 2216. Here, theflat surface of the micro-mirrors of the array 2218 is oriented parallelto the y-axis. Further here, the transmissive rim surface 2211 isconfigured as the surface 1511 of the intensity pattern 1810 describedabove in connection with FIG. 18C. As such, the tile borders 1813parallel to the y-axis are distributed at known angular locationsrelative to each other along the azimuthal θ-axis, and the tile borders1813 parallel to the x-axis are distributed at known axial locationsrelative to each other along the y-axis, so the intensity pattern 2210can be used as part of the displacement measuring system 2200 to measureboth an angular displacement Δθ of the wheel 2235 along the azimuthalθ-axis and an axial displacement ΔY of the wheel 2235 along the y-axis.

Moreover, the rim surface 2211 of the intensity pattern 2210 is spacedapart from and faces the LEE array 1804 and the photodetector 1522. Inthis manner, during operation of the displacement measuring system 2200,the LEE array 1804 illuminates the transmissive rim surface 2211 of theintensity pattern 2210 with N_(TOT) beams 1806; the transmissive rimsurface 2211 selectively transmits the N_(TOT) beams 1806; the array ofmicro-mirrors 2218 reflects, scatters or both the selectivelytransmitted beams, such that N_(TOT) redirected beams 1520A form anacute angle relative the selectively transmitted beams; and the rimsurface 2211 transmits the redirected beams 1520A to the photodetector1522A. In another implementation of the angular displacement measuringsystem 2200 (not illustrated in FIG. 22B), the intensity pattern 2210 isconfigured to have a selectively reflective rim surface 2211 asdescribed above in connection with FIG. 18C. During operation of thisimplementation of the angular displacement measuring system 2200, theLEE array 1804 illuminates the reflective rim surface 2211 of theintensity pattern 2210 with N_(TOT) beams 1806; and the reflective rimsurface 2211 selectively redirects (via reflection, scattering or both)the N_(TOT) beams 1806 to the photodetector 1522, such that the N_(TOT)redirected beams 1520A form an acute angle relative the beams 1806.

Further in the example shown in FIGS. 22A-22B, the LEE array 1804illuminates an area 1814 of the rim surface 2211 of the intensitypattern 2210 with N_(TOT) beams 1806, and separation along the azimuthalθ-axis and the y-axis between the illuminated locations 1808 areseparations δ_(θ) and δ_(Y)y. Moreover, the size along the azimuthalθ-axis and the size along the y-axis of each of tiles 1812 canaccommodate 2≤N≤N_(X,Y) concurrently illuminated locations 1808.

In this manner, the PWM driver 1536 of the displacement measuring system2200 can use a switching gate, similar to the switching gate 1524 shownin FIG. 15E, to time multiplex the N_(TOT) LEEs 1828 of the LEE array1804. In this manner, the processor 1546 (in conjunction with thephotodetector 1522) obtains, for each sampling time t_(k), an associatedset of N_(TOT) intensity values corresponding to intensities ofrespective beams 1520A redirected by the intensity pattern 2210 viaeither reflection off a selectively reflective rim surface 2211 at theilluminated locations 1808, or transmission through a selectivelytransmissive rim surface 2211 at the illuminated locations 1808. Assuch, the processor 1546 of the displacement measuring system 2200 candetermine, for each sampling time t_(k), positions along both theazimuthal θ-axis and axial y-axis of the illuminated locations 1808 ofthe rim surface 2211 of the intensity pattern 2210 based on relativedifferences between the intensity values of the associated obtained set.Then, in a manner similar to the manner described above in connectionwith FIGS. 18C-18E (e.g., by substituting ΔX with Δθ), the processor1546 determines, for each sampling time t_(k), both an angulardisplacement Δθ and an axial displacement ΔY of the wheel 2235 based onone or more changes of the intensity values of the issued set caused byrotation of the wheel that sweeps at least one of the tile borders 1813through at least one of the illuminating beams 1806.

Each of the intensity pattern 1510A/1510B illustrated in FIG. 15C, theintensity pattern 1710 illustrated in FIG. 17A, and the intensitypattern 1810 illustrated in FIG. 18C can be fabricated using infra-red(IR) ink with varying thickness based on various photo-mask processes,for instance. In some implementations, multiple masks can be applied toproduce the 1D 3-level intensity pattern 1710 as shown in FIG. 17A, orthe 2D 4-level intensity pattern 1810 shown in FIG. 18C. Commerciallyavailable IR inks used in visible light pass-through filters have stopbands in the range of 800 nm. IR VCSELs that emit light in the range of800-1100 nm are readily available. Processes for spin coating (forthickness and uniformity control) and photo mask (UV development)patterning, used to make CMOS image sensor color filter arrays (CFA),can be applied to the above-noted IR inks to fabricate the intensitypatterns 1510A/1510B, 1710, and 1810 with a spatial resolution of order˜1 μm. Alternatively, in the case of cost-sensitive applications, inkjetprinting can be used to fabricate the intensity patterns 1510A/1510B,1710, and 1810 with a spatial resolution of order ˜10 μm.

In some implementations, the controller system 1525 can be configured asmixed signal circuitry that processes analog signals and digitalsignals. In some implementations, the controller system 1525 can beconfigured as one or more digital signal processors, e.g., ASIC, FPGA,CPU, etc. In some implementations, at least portions of circuitry thatpowers and conditions the LEE array 1504/1804 can be combined with atleast portions of circuitry illustrated in FIG. 15D that is associatedwith the photodetector 1522 in a single system on a chip (SOC), ASIC,FPGA, CPU, etc.

A few embodiments have been described in detail above, and variousmodifications are possible. The disclosed subject matter, including thefunctional operations described in this specification, can beimplemented in electronic circuitry, computer hardware, firmware,software, or in combinations of them, such as the structural meansdisclosed in this specification and structural equivalents thereof,including system on chip (SoC) implementations, which can include one ormore controllers and embedded code.

While this specification contains many specifics, these should not beconstrued as limitations on the scope of what may be claimed, but ratheras descriptions of features that may be specific to particularembodiments. Certain features that are described in this specificationin the context of separate embodiments can also be implemented incombination in a single embodiment. Conversely, various features thatare described in the context of a single embodiment can also beimplemented in multiple embodiments separately or in any suitablesubcombination. Moreover, although features may be described above asacting in certain combinations and even initially claimed as such, oneor more features from a claimed combination can in some cases be excisedfrom the combination, and the claimed combination may be directed to asubcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various systemcomponents in the embodiments described above should not be understoodas requiring such separation in all embodiments.

Other embodiments fall within the scope of the following claims.

What is claimed is:
 1. A displacement measuring system comprising: (i) aback electromotive force (bEMF) sensing system to acquire a firstdisplacement signal that relates to a time dependence of a displacementof a mass, wherein the displacement is relative to a datum of thedisplacement measuring system; (ii) an optical sensing system comprisingan intensity pattern that is coupled with the mass and comprises two ormore tiles separated from each other by corresponding one or more tileborders, wherein the tile borders are at known locations relative toeach other; a light source that is at rest relative to the datum toilluminate the intensity pattern with a light beam, wherein multipletile border crossings occur while the first displacement signal is beingacquired, wherein a tile border crossing is said to occur when a tileborder of the intensity pattern crosses through the light beam; and aphotodetector that is at rest relative to the datum to acquire anintensity signal corresponding to intensity of the light beam redirectedto the photodetector from the intensity pattern, wherein the intensitysignal is indicative of the tile border crossings; and (iii) a processorto spatially resolve the tile border crossings indicated by theintensity signal, at least in part, based on whether the firstdisplacement signal increases or decreases at a time when a tile bordercrossing has occurred; and determine the displacement of the mass basedon the spatially resolved tile border crossings.
 2. The system of claim1, wherein the processor to determine a second displacement signal usingthe spatially resolved tile border crossings; and determine thedisplacement of the mass by combining the first displacement signal andthe second displacement signal.
 3. The system of claim 2, wherein theprocessor to determine a scale factor equal to a ratio of a change inthe second displacement signal over a predetermined time interval and achange in the first displacement signal over the predetermined timeinterval, differentiate the first displacement signal, and scale thedifferentiated first displacement signal based on the scale factor priorto the combining of the first displacement signal and the seconddisplacement signal.
 4. The system of claim 3, wherein the processorupdates the scale factor when the first displacement signal over thepredetermined time interval exceeds a threshold change.
 5. The system ofclaim 2, wherein the bEMF sensing system to sample the firstdisplacement signal using a first sampling frequency, and the opticalsensing system to sample the intensity signal using a second samplingfrequency smaller than the first sampling frequency, thereby samples ofthe second displacement signal have the second sampling frequency. 6.The system of claim 5, wherein, to perform the combining of the firstdisplacement signal and the second displacement signal, the processor toinsert corresponding samples of the scaled differentiated firstdisplacement signal between samples of the second displacement signal.7. The system of claim 1, wherein each tile has a size larger than abeam spot formed by the light beam that illuminates the intensitypattern, and each tile is configured to redirect to the photodetectorlight having an intensity different from an intensity of lightredirected to the photodetector by any of its adjacent tiles.
 8. Thesystem of claim 7, wherein the intensity pattern is a binary intensitypattern in which each tile has only two adjacent tiles configured toredirect to the photodetector light having the same intensity.
 9. Thesystem of claim 7, wherein each tile is a hexagonal tile configured toredirect to the photodetector light having an intensity level that isone of (i) a minimum intensity level, (ii) a maximum intensity level,(iii) a first intermediate intensity level between the minimum intensitylevel and the maximum intensity level, and (iv) a second intermediateintensity level between the first intermediate intensity level and themaximum intensity level.
 10. The system of claim 9, wherein the firstdisplacement signal acquired by the bEMF sensing system represents thetime dependence of a component of the displacement of the mass along afirst direction, and the processor to (i) spatially resolve first tileborder crossings indicated by the intensity signal based on whether thefirst displacement signal increases or decreases at a time when a firsttile border crossing has occurred along the first direction, and (ii)determine the component of the displacement of the mass along the firstdirection based on the spatially resolved first tile border crossings;and (iii) spatially resolve second tile border crossings indicated bythe intensity signal based on changes between a pair of the minimumintensity level, the maximum intensity level, the first intermediateintensity level, and the second intermediate intensity level ofredirected light that is captured by the photodetector when a secondtile border crossing has occurred along a second direction orthogonal tothe first direction, and (iv) determine a component of the displacementof the mass along the second direction based on the spatially resolvedsecond tile border crossings.
 11. The system of claim 9, wherein thelight source to concurrently illuminate three tiles of the intensitypattern that are adjacent to each other, one of the three adjacent tilesilluminated with the light beam, and the other two of the three adjacenttiles respectively illuminated with two reference light beams, the tworeference light beams spaced apart from the light beam by a separationabout equal to a separation between adjacent tiles, and the light beamand the reference light beams to illuminate the three adjacent tileswith substantially equal intensities.
 12. The system of claim 11,wherein the light source to concurrently illuminate the three adjacenttiles in a time multiplexed manner.
 13. The system of claim 11, whereinthe photodetector to further acquire reference signals corresponding tointensities of respective reference light beams redirected to thephotodetector from the intensity pattern, and the optical sensing systemto sample the intensity signal using a second sampling frequency and thereference signals using a third sampling frequency smaller than thesecond sampling frequency.
 14. The system of claim 11, wherein theprocessor to compare measured values and expected values of differencesbetween intensity of the light beam redirected to the photodetector fromone of the three adjacent tiles and respective ones of the other two ofthe three adjacent tiles respectively illuminated with two referencelight beams, and the light source to adjust the intensity of the lightbeam based on the compared differences.
 15. The system of claim 1,wherein the photodetector comprises a photodiode.
 16. The system ofclaim 1, wherein the photodetector comprises a threshold module to applyone or more threshold values to each intensity value of the light beamredirected to, and measured by, the photodetector to issue acorresponding expected value of the intensity value.
 17. The system ofclaim 16, wherein the photodetector comprises a filter to adaptivelydetermine the one or more threshold values.
 18. The system of claim 16,wherein the one or more threshold values are predetermined.
 19. Thesystem of claim 1, wherein the light source comprises a vertical cavitysurface emitting laser (VCSEL) to emit the light beam.
 20. The system ofclaim 1, wherein the light source comprises a light emitting diode (LED)to emit probe light; and beam-shaping optics to form the light beam. 21.The system of claim 1, wherein the intensity pattern is reflective tothe light beam, and disposed on a surface of the mass.
 22. The system ofclaim 1, wherein the intensity pattern is transparent to the light beam,and the optical sensing system comprises an optical structure having afirst surface and a second, opposing surface, the intensity pattern isdisposed on the first surface of the optical structure, and the opticalstructure is attached to a surface of the mass adjacent the secondsurface of the optical structure.
 23. The system of claim 22, whereinthe optical structure comprises an array of micro-mirrors disposedbetween the first and second surfaces of the optical structure, and themicro-mirrors of the array are oriented to redirect to the photodetectorthe light beam that impinges on the array of micro-mirrors aftertransmission through the intensity pattern.
 24. The system of claim 22,wherein the optical structure comprises solid material that istransparent to the light beam.
 25. The system of claim 24, wherein theoptical sensing system comprises a diffusive film sandwiched between thesecond surface of the optical structure and the surface of the mass, andthe diffusive film is configured to redirect to the photodetector thelight beam that impinges on the diffusive film after transmissionthrough the intensity pattern.
 26. The system of claim 24, wherein thesecond surface of the optical structure is spaced apart from the surfaceof the mass by an air gap, and the second surface of the opticalstructure comprises facets arranged to reflect, via total internalreflection (TIR), to the photodetector, the light beam that impinges onthe facets after transmission through the intensity pattern.
 27. Thesystem of claim 24, wherein the optical sensing system comprises adiffusive material sandwiched between the second surface of the opticalstructure and the surface of the mass, and the second surface of theoptical structure comprises facets arranged to diffusely reflect, to thephotodetector, the light beam that impinges on the facets aftertransmission through the intensity pattern.
 28. A haptic enginecomprising the mass and the displacement measuring system recited inclaim
 1. 29. A computing device comprising the haptic engine of claim28.